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Ch. 8 Inferences Based on a Single Sample: Tests of Hypothesis

8.1 The Elements of a Test of Hypothesis

1 Write Null and Alternative Hypotheses

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.3 hours. In order to test whether the time to fill out the form has been reduced, a sample of 53 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 6.1 hours with a standard deviation of 2.6 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.

A) H0: = 6.3 B) H0: = 6.3 C) H0: = 6.3 D) H0: > 6.3 Ha: <6.3 Ha: >6.3 Ha: =6.3 Ha: <6.3
2) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 62 tissues during a cold. Suppose a random sample of 100 people yielded the following data on the
number of tissues used during a cold: x = 50, s = 16. Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than 62.
A) H0: = 62 vs. Ha: < 62 B) H0: = 62 vs. Ha: > 62 C) H0: = 62 vs. Ha: = 62 D) H0: > 62 vs. Ha: 62

3) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 34 minutes. The owner has randomly selected 19 customers and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful?

A) H0: = 34 vs. Ha: > 34 B) H0: = 34 vs. Ha: < 34 C) H0: = 34 vs. Ha: = 34 D) H0: < 34 vs. Ha: = 34
4) Researchers have claimed that the average number of headaches per student during a semester of Statistics is 10. Statistics students believe the average is higher. In a sample of n = 24 students the mean is 15 headaches with a deviation of 2. Which of the following represent the null and alternative hypotheses necessary to test the students' belief?
A) H0: = 10 vs. Ha: > 10 B) H0: < 10 vs. Ha: = 10 C) H0: = 10 vs. Ha: < 10 D) H0: = 10 vs. Ha: = 10
5) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but are now beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. What null and alternative hypothesis should be tested?
A) H0: = 215 vs. HA: = 215 B) H0: = 215 vs. HA: < 215 C) H0: = 215 vs. HA: > 215 D) H0: 215 vs. HA: < 215
Answer the question True or False.
6) The null hypothesis represents the status quo to the party performing the sampling experiment.
A) True
B) False
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7) The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false. A) True B) False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
8) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 17% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 74 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in ten. Specify the null and alternative hypotheses that the researchers wish to test.
9) According to an advertisement, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 594 bushels per acre. Twenty farmers who belong to a cooperative plant the soybeans in soil prepared as specified. Each uses a 40-acre plot and records the mean yield per acre. The mean
and variance for the sample of 20 farms are x = 550 and s2 = 10,000. Specify the null and alternative hypotheses used to determine if the mean yield for the soybeans is different than advertised.
2 Interpret Type I and Type II Errors
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
10) The owner of Get-A-Away Travel has recently surveyed a random sample of 480 customers to determine whether the mean age of the agency's customers is over 28. The appropriate hypotheses are H0: = 28,
Ha: > 28. If he concludes the mean age is over 28 when it is not, he makes a __________ error. If he concludes the mean age is not over 28 when it is, he makes a __________ error.

A) Type I; Type II B) Type II; Type II C) Type I; Type I D) Type II; Type I

11) An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 4 days, and an alternative hypothesis that the average time for processing a claim is greater than 4 days. After completing the statistical test, it is concluded that the average time exceeds 4 days. However, it is eventually learned that the mean process time is really 4 days. What type of error occurred in the statistical test?

A) Type I error B) Type II error

C) Type III error D) No error occurred in the statistical sense.

12) Suppose we wish to test H0: = 58 vs. Ha: > 58. What will result if we conclude that the mean is greater than 58 when its true value is really 63?

A) a correct decision B) a Type II error C) a Type I error D) none of the above

13) I want to test H0: p = .7 vs. Ha: p = .7 using a test of hypothesis. If I concluded that p is .7 when, in fact, the true

value of p is not .7, then I have made a __________.

A) Type II error B) Type I error

C) correct decision D) Type I and Type II error

14) A significance level for a hypothesis test is given as = .01. Interpret this value. A) The probability of making a Type I error is .01.

B) The smallest value of that you can use and still reject H0 is .01. C) The probability of making a Type II error is .99.

D) There is a 1% chance that the sample will be biased.

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15) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 12 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of

n = 133 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 11.2 mph, with a standard deviation of s = 2.7 mph. To determine whether the site meets the organizations requirements, consider the test, H0: = 12 vs. Ha: > 12, where is the true mean wind speed at the site and = .05. Fill in

the blanks. A Type I error in the context of this problem is to conclude that the true mean wind speed at the site _____ 12 mph when it actually _____ 12 mph.

A) exceeds; equals B) equals; exceeds C) equals; equals

16) If I specify to be .36, then the value of must be .64.

A) True B) False

17) What is the probability associated with not making a Type II error? A) (1 ) B) C)

D) exceeds; exceeds

D) (1 ) A) = p(Type II error) is not known. B) = p(Type I error) is not known.

18) We never conclude Accept H0 in a test of hypothesis. This is because:

C) H0 is never true. D) We want H0 to be false.

19) A __________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

A) test statistic B) critical value C) parameter D) significance level

20) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associations name. The associations by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses:

H0: p = 0.6 HA: p > 0.6

Define a Type I Error in the context of this problem.

A) They conclude that more than 60% of the association wants a name change when that is, in fact, true.

B) They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

C) They conclude that more than 60% of the association wants a name change when, in fact, that is not true. D) They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

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21) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associations name. The associations by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses:

H0: p = 0.6 HA: p > 0.6

Define a Type II Error in the context of this problem.

A) They conclude that more than 60% of the association wants a name change when that is, in fact, true.

B) They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

C) They conclude that more than 60% of the association wants a name change when, in fact, that is not true. D) They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

Answer the question True or False.

22) We do not accept H0 because we are concerned with making a Type II error. A) True B) False

23) In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true.

A) True B) False

24) A Type I error occurs when we accept a false null hypothesis.

A) True B) False

25) The rejection region refers to the values of the test statistic for which we will reject the alternative hypothesis. A) True B) False

8.2 Formulating Hypotheses and Setting Up the Rejection Region

1 Identify Rejection Region

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the rejection region for the specified hypothesis test.

1) Consider a test of H0: = 10. For the following case, give the rejection region for the test in terms of the z-statistic: Ha: > 10, = 0.01

A) z > 2.33 B) z > 2.05 C) |z| > 2.575 D) |z| > 2.33

2) Consider a test of H0: = 4. For the following case, give the rejection region for the test in terms of the z-statistic: Ha: < 4, = 0.08
A) z < -1.41 B) z > -1.41 C) z < -1.75 D) z < 1.75
3) Consider a test of H0: = 7. For the following case, give the rejection region for the test in terms of the z-statistic: Ha: = 7, = 0.01
A) |z| > 2.575 B) z > 2.575 C) z > 2.33 D) |z| > 2.33

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

4) The hypotheses for H0: = 65 and Ha: > 65 are tested at = .05. Sketch the appropriate rejection region. Page 194

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5) The hypotheses for H0: = 125.4 and Ha: = 125.4 are tested at = .10. Sketch the appropriate rejection region. For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.

6) z > 2.575 7) z < -1.28 8) z < -1.96
9) z < -2.33 or z > 2.33 10) z < -2.05 or z > 2.05

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

11) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 50 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on

the number of tissues used during a cold: x = 45, s = 18. Using the sample information provided, set up the calculation for the test statistic for the relevant hypothesis test, but do not simplify.

A)z= 45-50 B)z=45-50 C)z= 45-50 D)z=45-50 18 18 18 182

10,000 10,0002 10,000

12) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 66 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on

the number of tissues used during a cold: x = 61, s = 25. We want to test the alternative hypothesis Ha: < 66. State the correct rejection region for = .05.
A) Reject H0 if z < -1.645. B) Reject H0 if z > 1.645. C) Reject H0 if z > 1.96 or z < -1.96. D) Reject H0 if z < -1.96.
13) The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Identify the null and alternative hypothesis that should be tested to determine if a name change is warranted.
A) H0: p = 0.6 vs. Ha: p = 0.6 C) H0: p = 0.6 vs. Ha: p < 0.6
B) H0: p = 0.6 vs. Ha: p > 0.6 D) H0: p 0.6 vs. Ha: p < 0.6
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14) Consider the following printout. HYPOTHESIS: VARIANCE X = x X =
SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) =
VARIANCE X - x = z =
gpa
2.2911 .18000 199 2.4
-.1089 -3.62091
Suppose we tested Ha: < 2.4. Find the appropriate rejection region if we used = .05.
A) Reject if z < -1.645. B) Reject if z > 1.645 or z < -1.645.
C) Reject if z > 1.96 or z < -1.96. D) Reject if z < -1.96.
Answer the question True or False.
15) A rejection region is established in each tail of the sampling distribution for a two-tailed test. A) True B) False
16) The rejection region for a two-tailed test with = .05 is -1.96 < z < 1.96. A) True B) False
8.3 Test of Hypothesis about a Population Mean: Normal (z) Statistic
1 Perform Hypothesis Test for Population Mean
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 69 tissues during a cold. Suppose a random sample of 2500 people yielded the following data on the
number of tissues used during a cold: x = 60, s = 16. Suppose the corresponding test statistic falls in the rejection region at = .05. What is the correct conclusion?
A) At = .05, reject H0. B) At = .10, reject H0. C) At = .05, accept Ha. D) At = .10, reject Ha.
2) We have created a 99% confidence interval for with the result (10, 15). What conclusion will we make if we test H0: = 17 vs. Ha: = 17 at = .01?
A) Reject H0 in favor of Ha. B) Accept H0 rather than Ha.
C) Fail to reject H0.
D) We cannot tell what our decision will be with the information given.
3) Suppose we wish to test H0: = 23 vs. Ha: < 23. Which of the following possible sample results gives the most evidence to support Ha (i.e., reject H0)?
A) x = 19, s = 5 B) x = 20, s = 8
C) x = 21, s = 6 D) x = 19, s = 11
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4) Consider the following printout. HYPOTHESIS: VARIANCE X = x X =
SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) =
VARIANCE X - x = z =
gpa
3.3531 .17000 206 3.5
-.1469 -5.11365
State the proper conclusion when testing H0: = 3.5 vs. Ha: < 3.5 at = .05. A) Reject H0.
B) Fail to reject H0.
C) Accept H0.
D) We cannot determine from the information given.
5) Consider the following printout. HYPOTHESIS: VARIANCE X = x X =
SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) =
VARIANCE X - x = z =
gpa
2.1862 .20000 167 2.3
-.1138 -3.28841
Is this a large enough sample for this analysis to work? A) Yes, since n = 167, which is greater than 30.
B) Yes, since the np > 15 and nq > 15.

C) Yes, since the population of GPA scores is approximately normally distributed. D) No.

6) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 16 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of

n = 50 wind speed recordings (taken at random intervals), the wind speed at the site averaged x = 16.7 mph, with a standard deviation of s = 3.6 mph. To determine whether the site meets the organizations requirements, consider the test, H0: = 16 vs. Ha: > 16, where is the true mean wind speed at the site and = .01.

Suppose the value of the test statistic were computed to be 1.37. State the conclusion.

A) At = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph.

B) At = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 16 mph. C) We are 99% confident that the site meets the organizations requirements.

D) We are 99% confident that the site does not meet the organizations requirements.

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7) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the universitys students differed from 20 minutes. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.05.

A) Reject H0 if z < -1.645 or z > 1.645. B) Reject H0 if z < -1.96 or z > 1.96. C) Reject H0 if z > 1.645. D) Reject H0 if z < -1.96.
8) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test.
A) z = 2.437 B) z = 37.59 C) z = 0.173 D) z = 2.551
9) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 200 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find the large-sample rejection region appropriate for this test if we are using = 0.05.
A) Reject H0 if z < -1.645 or z > 1.645. B) Reject H0 if z < -1.96 or z > 1.96. C) Reject H0 if z > 1.645. D) Reject H0 if z < -1.96.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
10) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 67 hours. In order to test whether the time to fill out the form has been reduced, a sample of 81 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 66.7 hours with a standard deviation of 15 hours. State the rejection region for the desired test at = .10.
11) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 940 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 940 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .01 significance level. Suppose 99 bulbs
were tested with the following results: x = 962 hours, s = 77 hours. Find the rejection region for the test of interest to the State University.
12) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. Suppose 121 bulbs
were tested with the following results: x = 827.5 hours, s = 110 hours. Conduct the test using = .05.
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13) The scores on a standardized test are reported by the testing agency to have a mean of 70. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test.
39 48 55 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 91 92 92 93 95 96 97 97 99
Use the data to conduct a test of hypotheses at = .05 to determine whether there is any evidence to support the counselor's suspicions.
14) A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below.
4.4 4.7 4.6 4.4 4.5 4.3 4.6 4.5 4.6 4.9 4.6 4.8 4.3 4.4 4.7 4.5 4.2 4.3 4.1 4.0 4.5 4.6 4.2 4.4 4.7 4.8 5.0 4.2 4.1 4.5
Test whether the population mean weight of the chickens is less than 4.6 pounds. Use = .05.
8.4 Observed Significance Levels: p-Values
1 Determine if Null Hypothesis is Rejected Given and p-Value
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
For the given value of and observed significance level (p -value), indicate whether the null hypothesis would be rejected.
1) = 0.08, p-value = 0.001 A) Reject H0
2) = 0.08, p-value = 0.10 A) Fail to reject H0
Solve the problem.
B) Fail to reject H0
B) Reject H0
3) Consider a test of H0: = 65 performed with the computer. SPSS reports a two-tailed p-value of 0.0892. Make the appropriate conclusion for the given situation: Ha: < 65, z = -1.7, = 0.05
A) Reject H0 B) Fail to reject H0
4) Consider a test of H0: = 30 performed with the computer. SPSS reports a two-tailed p-value of 0.0164. Make the appropriate conclusion for the given situation: Ha: > 30, z = -2.4, = 0.01

A) Fail to reject H0 B) Reject H0

5) Consider a test of H0: = 70 performed with the computer. SPSS reports a two-tailed p-value of 0.2302. Make the appropriate conclusion for the given situation: Ha: > 70, z = 1.20, = 0.10

A) Fail to reject H0

B) Reject H0

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6) Consider a test of H0: = 80 performed with the computer. SPSS reports a two-tailed p-value of 0.0038. Make the appropriate conclusion for the given situation: Ha: = 80, z = 2.9, = 0.04

A) Reject H0 B) Fail to reject H0

7) Given H0: = 25, Ha: = 25, and p = 0.034. Do you reject or fail to reject H0 at the .01 level of significance? A) fail to reject H0

B) reject H0

C) not sufficient information to decide

8) Given H0: = 18, Ha: < 18, and p = 0.068. Do you reject or fail to reject H0 at the .05 level of significance? A) fail to reject H0
B) reject H0
C) not sufficient information to decide
9) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 49 bottles and finds the average amount of liquid held by the bottles is 9.9155 ounces with a standard deviation of 0.35 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion.
A) At = 0.05, reject the null hypothesis. B) At = 0.035, accept the null hypothesis. C) At = 0.085, fail to reject the null hypothesis. D) At = 0.025, reject the null hypothesis.
10) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. The information was entered into a spreadsheet and the following printout was obtained:
One-Sample T Test
Null Hypothesis: = 215
Alternative Hyp: > 215

Variable Mean SE Lower Upper T DF P

95% Conf Interval Camera Price 245.23 15.620 212.740 277.720 1.94 21 0.0333

Cases Included 22

Use the p- value given above to determine which of the following conclusions is correct.

A) At = 0.01, there is sufficient evidence to indicate that the mean price of all digital cameras exceeds

$215.00

B) At = 0.05, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds

$215.00

C) At = 0.10, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds

$215.00

D) At = 0.03, there is insufficient evidence to indicate that the mean price of all digital cameras exceeds

$215.00

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11) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used to create a confidence interval and to conduct a test of hypothesis, both of which are shown in the printout below.

One-Sample Z Test Null Hypothesis: = 20

Alternative Hyp: > 20

Variable Mean SE Lower Upper Z P

95% Conf Interval Camera Price 23.243 1.3133 20.669 25.817 2.47 0.0071

Cases Included 238

What conclusion can be made from the test of hypothesis conducted in this printout? Begin each answer with, When testing at = 0.01

A) there is sufficient evidence to indicate that the average travel time of all students is equal to 20 minutes.

B) there is insufficient evidence to indicate that the average travel time of all students exceeds 20 minutes.

C) there is sufficient evidence to indicate that the average travel time of all students exceeds 20 minutes.

D) there is insufficient evidence to indicate that the average travel time of all students is equal to 20

minutes.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

12) Based on the information in the screen below, what would you conclude in the test of H0: 14, Ha: > 14. Use = .01.

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2 Find and Interpret p-Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

13) Consider the following printout. HYPOTHESIS: MEAN X = x

X =

SAMPLE MEAN OF X = SAMPLE VARIANCE OF X = SAMPLE SIZE OF X = HYPOTHESIZED VALUE (x) =

A) p = 0.2006 B) p = 0.1003 C) p = 0.8997 D) p = 0.7994

14) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 10 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organizations requirements, consider the test, H0: = 10 vs. Ha: > 10, where is the true

mean wind speed at the site and = .01. Suppose the observed significance level (p-value) of the test is calculated to be p = 0.2991. Interpret this result.

A) Since the p-value exceeds = .01, there is insufficient evidence to reject the null hypothesis. B) The probability of rejecting the null hypothesis is 0.2991.

C) We are 70.09% confident that = 10.

D) Since the p-value greatly exceeds = .01, there is strong evidence to reject the null hypothesis.

15) If a hypothesis test were conducted using = 0.05, to which of the following p-values would cause the null hypothesis to be rejected.

A) 0.040 B) 0.060 C) 0.100 D) 0.055

16) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Suppose a sample of 108 students produced a test statistic of z = -1.35. Find the p-value for the test of interest to the college.

A) p = 0.4115 B) p = 0.9115 C) p = 0.1770 D) p = 0.0885

17) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the universitys students differed from 20 minutes. Suppose the large-sample test statistic was calculated to be z = 2.14. Find the p-value for this test of hypothesis.

A) p = 0.4838 B) p = 0.9838 C) p = 0.0162 D) p = 0.0324

Answer the question True or False.

18) The smaller the p-value in a test of hypothesis, the more significant the results are.

MEAN X x = z =

gpa

2.9528 0.226933 167

3 -0.0472

-1.2804

Suppose a two-tailed test is desired. Find the p-value for the test.

A) True

B) False

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

19) In a test of H0: = 65 against Ha: > 65, the sample data yielded the test statistic z = 1.38. Find and interpret the p-value for the test.

20) In a test of H0: = 70 against Ha: =70, the sample data yielded the test statistic z = 2.11. Find and interpret the p-value for the test.

21) In a test of H0: = 12 against Ha: > 12, a sample of n = 75 observations possessed mean x = 13.1 and standard deviation s = 4.3. Find and interpret the p-value for the test.

22) In a test of H0: = 250 against Ha: = 250, a sample of n = 100 observations possessed mean x = 247.3 and standard deviation s = 11.4. Find and interpret the p-value for the test.

23) The scores on a standardized test are reported by the testing agency to have a mean of 75. Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test.

39 48 55 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 91 92 92 93 95 96 97 97 99

Find and interpret the p-value for the test of H0: = 75 against Ha: > 75.

24) A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the stores chickens yielded the weights (in pounds) shown below.

4.4 4.7 4.6 4.4 4.5 4.3 4.6 4.5 4.6 4.9 4.6 4.8 4.3 4.4 4.7 4.5 4.2 4.3 4.1 4.0 4.5 4.6 4.2 4.4 4.7 4.8 5.0 4.2 4.1 4.5

Find and interpret the p-value in a test of H0: = 4.6 against Ha: < 4.6.
8.5 Test of Hypothesis about a Population Mean: Student's t-Statistic
1 Perform Hypothesis Test for Population Mean
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 30 minutes. The owner has randomly selected 17 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 30 minutes. What assumption is necessary for this test to be valid?
A) The population of delivery times must have a normal distribution. B) The population variance must equal the population mean.
C) The sample mean delivery time must equal the population mean delivery time. D) None. The Central Limit Theorem makes any assumptions unnecessary.
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2) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 35 minutes. The owner has randomly selected 24 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 35 minutes. Suppose the p-value for the test was found to be .0274. State the correct conclusion.
A) At = .025, we fail to reject H0. B) At = .05, we fail to reject H0. C) At = .02, we reject H0. D) At = .03, we fail to reject H0.
3) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties.
HYPOTHESIS: MEAN X = x
X = land_value
SAMPLE MEAN OF X = 51,288 SAMPLE VARIANCE OF X = 273,643,254
SAMPLE SIZE OF X = 25
x = 46,845
MEAN X - x = 4443
t = 1.34293
D.F. = 24 P-VALUE = 0.1918585
P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43
Suppose we are interested in testing whether the mean land value from this neighborhood differs from 46,845. Which hypotheses would you test?
A) H0: = 46,845 vs. Ha: = 46,845 B) H0: = 46,845 vs. Ha: > 46,845 C) H0: = 46,845 vs. Ha: < 46,845 D) H0: = 46,845 vs. Ha: = 46,845
4) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties.
HYPOTHESIS: MEAN X = x
X = land_value
SAMPLE MEAN OF X = 50,098 SAMPLE VARIANCE OF X = 273,643,254
SAMPLE SIZE OF X = 25
x = 45,655
MEAN X - x = 4443
t = 1.34293
D.F. = 24 P-VALUE = 0.1918585
P-VALUE/2 = 0.0959288 SD. ERROR = 3308.43
Find the p-value for testing whether the mean land value differs from $45,655.
A) p = 0.1918585 B) p = 0.0959288 C) p = 0.808142 D) p = 0.308142
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5) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties.
HYPOTHESIS: MEAN X = x X
SAMPLE MEAN OF X SAMPLE VARIANCE OF X SAMPLE SIZE OF X x
MEAN X - x t D.F. P-VALUE P-VALUE/2 SD. ERROR
= land_value
= 51,315
= 273,643,254 = 25
= 46,872
= 4443
= 1.34293
= 24
= 0.1918585 = 0.0959288 = 3308.43
What is the correct conclusion when testing a greater-than alternative hypothesis at = .01?
A) Fail to reject H0. B) Accept H0. C) Reject H0. D) Fail to reject Ha.
6) Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties.
HYPOTHESIS: MEAN X = x X
SAMPLE MEAN OF X SAMPLE VARIANCE OF X SAMPLE SIZE OF X x
MEAN X - x t D.F. P-VALUE P-VALUE/2 SD. ERROR
= land_value
= 51,860
= 273,643,254 = 25
= 47,417
= 4443
= 1.34293
= 24
= 0.1918585 = 0.0959288 = 3308.43
What assumptions are necessary
A) The sample was selected from an approximately normal population.
for any inferences derived from this printout to be valid?
B) None. The Central Limit Theorem makes any assumptions unnecessary. C) The sampled data are approximately normal.
D) The sampling distribution of the sample mean is approximately normal.
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7) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 14 ounces printed on each cartridge. To check this claim, a sample of n = 17 cartridges are randomly selected from the shipment and
carefully weighed. Summary statistics for the sample are: x = 14.1 ounces, s = .17 ounce. To determine whether the supplier's claim is true, consider the test, H0: = 14 vs. Ha: > 14, where is the true mean weight of the

cartridges. Calculate the value of the test statistic.

A) 2.425 B) 1.000 C) 10.000 D) 0.588

8) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 10 ounces printed on each cartridge. To check this claim, a sample of n = 10 cartridges are randomly selected from the shipment and

carefully weighed. Summary statistics for the sample are: x = 10.11 ounces, s = .30 ounce. To determine whether the suppliers claim is true, consider the test, H0: = 10 vs. Ha: > 10, where is the true mean weight of the

cartridges. Find the rejection region for the test using = .01.

A) t > 2.821, where t depends on 9 df B) z > 2.33

C) |z| > 2.58 D) t > 3.25, where t depends on 9 df

9) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 25 bottles and finds the average amount of liquid held by the bottles is 9.8 ounces with a standard deviation of .4 ounce. Which of the following is the set of hypotheses the company wishes to test?

A) H0: = 10 vs. Ha: < 10 B) H0: < 10 vs. Ha: = 10 C) H0: = 10 vs. Ha: > 10 D) H0: = 10 vs. Ha: = 10

10) A bottling company produces bottles that hold 8 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 24 bottles and finds the average amount of liquid held by the bottles is 7.6 ounces with a standard deviation of .3 ounce. Calculate the appropriate test statistic.

A) t=-6.532 B) t=-32.000 C) t=-3.578 D) t=-6.394

11) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this test if we are using = 0.05.

A) Reject H0 if t > 1.725 C) Reject H0 if t > 1.717

B) Reject H0 if t > 2.080 or t < -2.080 D) Reject H0 if t > 1.721

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12) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. The information was entered into a spreadsheet and the following printout was obtained:

One-Sample T Test

Null Hypothesis: = 215

Alternative Hyp: > 215

Variable Mean SE

Camera Price 245.23 15.620

Cases Included 22

95% Conf Interval

Lower Upper

212.740 277.720 1.94 21 0.0333

Is a sample size n = 22 large enough to utilize the central limit theorem in this inferential procedure? A) Yes, since both np and nq are greater than or equal to 15

B) No, since n < 30
C) No, since either np or nq is less than 15
D) Yes, since the central limit theorem works whenever means are used
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
13) According to an advertisement, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 107 bushels per acre. Twenty farmers who belong to a cooperative plant the soybeans in soil prepared as specified. Each uses a 40-acre plot and records the mean yield per acre. The mean
and variance for the sample of the 20 farms are x = 92 and s2 = 18,000. Find the rejection region used for determining if the mean yield for the soybeans is not equal to 107 bushels per acre. Use = .05.
14) A random sample of n = 12 observations is selected from a normal population to test H0: = 22.1 against Ha: > 22.1 at = .05. Specify the rejection region.

15) A random sample of n = 18 observations is selected from a normal population to test H0: = 145 against Ha: = 145 at = .10. Specify the rejection region.

16) A random sample of n = 15 observations is selected from a normal population to test H0: = 2.89 against Ha: < 2.89 at = .01. Specify the rejection region.
17) A sample of 6 measurements, randomly selected from a normally distributed population, resulted in the
following summary statistics: x = 9.1, s = 1.5. Test the null hypothesis that the mean of the population is 10 against the alternative hypothesis < 10. Use = .05.
18) A sample of 8 measurements, randomly selected from a normally distributed population, resulted in the
following summary statistics: x = 5.2, s = 1.1. Test the null hypothesis that the mean of the population is 4 against the alternative hypothesis = 4. Use = .05.
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19) A recipe submitted to a magazine by one of its subscribers states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed.
54 55 58 59 59 60 61 61 62 65
Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking
time is 55 minutes against the alternative hypothesis > 55. Use = .05.

20) An ink cartridge for a laser printer is advertised to print an average of 10,000 pages. A random sample of eight businesses that have recently bought this cartridge are asked to report the number of pages printed by a single cartridge. The results are shown.

9771 9811 9885 9914 9975 10,079 10,145 10,214

Assume that the data belong to a normal population. Test the null hypothesis that the mean number of pages is 10,000 against the alternative hypothesis = 10,000. Use = .10.

21) A random sample of 8 observations from an approximately normal distribution is shown below. 56458653

Find the observed level of significance for the test of H0: = 5 against Ha: = 5. Interpret the result.

22) Based on the information in the screen below, what would you conclude in the test of H0: 14, Ha: > 14.

Use = .01.

8.6 Large-Sample Test of Hypothesis about a Population Proportion

1 Perform Hypothesis Test for Population Proportion

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For the given binomial sample size and null-hypothesized value of p0, determine whether the sample size is large enough to use the normal approximation methodology to conduct a test of the null hypothesis H0: p = p0.

1) n = 100, p0 = 0.4 A) Yes

2) n = 70, p0 = 0.9 A) No

3) n = 700, p0 = 0.01 A) No

B) No

B) Yes

B) Yes

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4) n = 1100, p0 = 0.99

A) No B) Yes

Solve the problem.

5) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have laptops. Find the rejection region for the corresponding test using = .10.

A) Reject H0 if z > 1.28. B) Reject H0 if z < -1.28. C) Reject H0 if z > 1.645 or z < -1.645. D) Reject H0 if z = 1.28.
6) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
A) .0164 B) .0082 C) .4836 D) .4918
7) The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 65 have laptops. What assumptions are necessary for this test to be satisfied?
A) The sample size n satisfies both np0 15 and nq0 15.
B) The population has an approximately normal distribution. C) The sample proportion is close to .5.
D) The sample size n satisfies n 30.
8) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 83 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately:
A) -2.33 B) 2.33 C) -1.83 D) -1.99
9) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z = -2.23. Can we conclude that H0 should be rejected at the a) = .10,
b) = .05, and c) = .01 level? A) a) yes; b) yes; c) no
C) a) no; b) no; c) no
B) a) yes; b) yes; c) yes D) a) no; b) no; c) yes
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10) A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda.
HYPOTHESIS: PROPORTION X = x
X = drink_(soda=1)
SAMPLE PROPORTION OF X = .419162 SAMPLE SIZE OF X = 167
HYPOTHESIZED VALUE (x) = .5
SAMPLE PROPORTION X - x = -.080838 Z = -2.08932
P-VALUE = .0366 P-VALUE/2 = .0183
SD. ERROR = .0386912
State the proper conclusion if the test was conducted at = .10.
A) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of
soda differs from .50.
B) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of
soda is less than .50.
C) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of
soda is less than .50.
D) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of
soda differs from .50.
11) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.02.
A) Reject H0 if z < -2.055. C) Reject H0 if z < -2.326.
B) Reject H0 if z < -2.326 or z > 2.326. D) Reject H0 if z < -1.96.
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12) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained:
Hypothesis Test - One Proportion
Sample Size 108 Successes 16 Proportion 0.14815
Null Hypothesis: P=0.2 Alternative Hyp: P<0.2
Difference -0.05185 Standard Error 0.03418
Z -1.35 p-value
0.0885
Based on the information contained in the printout, what conclusion would be correct when testing at = 0.05. A) Reject H0 B) Fail to reject H0 C) Accept H0 D) Accept HA
13) A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. The college decided to take a random sample of 108 of their current students to use in the analysis. Is the sample size of n = 108 large enough to use this inferential procedure?
A) No
B) Yes, since n 30
C) Yes, since both np and nq are greater than or equal to 15
D) Yes, since the central limit theorem works whenever proportions are used
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
14) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 60 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 7. Calculate the test statistic used by the researchers for the corresponding test of hypothesis.
15) A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 9. Is the sample size sufficiently large to conduct this test of hypothesis? Explain.
16) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits. A random sample of 250 manufacturing firms is selected, and only 27 of them offer child-care benefits. Specify the rejection region that the union will use when testing at = .05.
17) Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits. A random sample of 320 manufacturing firms is selected and asked if they offer child-care benefits. Suppose the p-value for this test was reported to be p = .1124. State the conclusion of interest to the union. Use = .10.
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
18) I want to test H0: p = .7 vs. Ha: p = .7 using a test of hypothesis. This test would be called a(n) ____________ test.
A) two-tailed B) one-tailed C) upper-tailed D) lower-tailed SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
19) A company reports that 80% of its employees participate in the company's stock purchase plan. A random sample of 50 employees was asked the question, "Do you participate in the stock purchase plan?" The answers are shown below.
yes no no yes no no yes yes no no no yes yes yes no yes no no yes yes no yes yes no yes yes no yes yes yes yes no no yes yes yes yes yes no yes no yes yes no yes yes yes yes yes yes
Perform the appropriate test of hypothesis to investigate your suspicion that fewer than 80% of the company's employees participate in the plan. Use = .05.
20) A random sample of 100 observations is selected from a binomial population with unknown probability of success, p. The computed value of p^ is equal to .56. Find the observed levels of significance in a test of
H0: p = .5 against Ha: p > .5. Interpret the result.

21) Identify the observed level of significance for the test summarized on the screen below and interpret its value.

8.7 Calculating Type II Error Probabilities: More about (Optional)

1 Find and Interpret

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) It is desired to test H0: = 45 against Ha: < 45 using = .10. The population in question is uniformly
distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If is really equal to 40, what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
A) .1469 B) .8531 C) .3531 D) .2938
2) It is desired to test H0: = 12 against Ha: = 12 using = 0.05. The population in question is uniformly
distributed with a standard deviation of 2.0. A random sample of 100 will be drawn from this population. If is really equal to 11.9, what is the value of associated with this test?
A) .9209 B) .0791
C) .4210 D) .0395
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3) It is desired to test H0: = 50 against HA: = 50 using = 0.10. The population in question is uniformly
distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If is really equal to 48, what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
A) 0.7567 B) 0.2433 C) 0.8994 D) 0.1006 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) It has been estimated that the G-car obtains a mean of 40 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 64 G-cars and records the mileage obtained for each car over a driving course
similar to that used to obtain the estimate. The following data resulted: x = 41.5 miles per gallon, s = 8 miles per gallon. Calculate the value of if the true value of the mean is 42 miles per gallon. Use = .025.
2 Find and Interpret Power of Test
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
5) It is desired to test H0: = 55 against Ha: < 55 using = .10. The population in question is uniformly
distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If is really equal to 50, what is the power of this test?
A) .8531 B) .1469 C) .2938 D) .3531
6) It is desired to test H0: = 50 against HA: = 50 using = 0.10. The population in question is uniformly
distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If is really equal to 45, what is the power of the test?
A) 0.2456 B) 0.7544 C) 0.8959 D) 0.1041
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
7) It has been estimated that the G-car obtains a mean of 30 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 36 G-cars and records the mileage obtained for each car over a driving course
similar to that used to obtain the estimate. The following data resulted: x = 31.8 miles per gallon, s = 6 miles per gallon. Calculate the power of the test if the true value of the mean is 31 miles per gallon. Use a value of
= .025.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Answer the question True or False.
8) The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean 0.
A) True B) False
9) Type I errors and Type II errors are complementary events so that = P(Type I error) = 1 - P(Type II error) = 1 - .
A) True B) False
10) Under the assumption that = a, where a is the alternative mean, the distribution of x is mound shaped and symmetric about a.
A) True
B) False
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11) The value of is the area under the bell curve for the distribution of x centered at a for values of x that fall
within the acceptance region of the distribution of x centered at 0. A) True B) False
8.8 Test of Hypothesis about a Population Variance (Optional)
1 Use Chi-Square Distribution
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.
1) Let 20 be a particular value of 2. Find the value of 20 such that P( 2> 20 ) = .10 for n = 10.

A) 14.6837 B) 4.16816 C) 15.9871 D) 16.919

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

2) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .08 to ensure proper inoculation. A random sample of 25 injections resulted in a variance of .103. Calculate the test statistic for the test of interest.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

3) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0:

2 = 155. Specify the appropriate rejection region. Ha: 2 < 155, n = 14, = .01
A) 2 < 4.10691 B) 2 < 27.6883 C) 2 < 4.66043 D) 2 < 29.1413
4) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0:
2 = 155. Specify the appropriate rejection region. Ha: 2 = 155, n = 10, = .05
A) 2 < 2.70039 or 2 > 19.0228 B) 2.70039 < 2 < 19.0228
C) 2 < 3.32511 or 2 > 16.9190 D) 2 < 3.24697 or 2 > 20.4831

5) A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0: 2 = 155. Specify the appropriate rejection region.

Ha: 2 > 155, n = 25, = .10

A) 2 > 33.1963 B) 2 > 34.3816 C) 2 > 36.4151 D) 2 > 15.6587

6) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was 23.243 minutes and the sample standard deviation was 20.40 minutes. Find the rejection region for determining if the population standard deviation exceeds 20 minutes. Use = 0.05.

A) Reject H0 if z > 1.645

C) Reject H0 if 2 > 71.4202

B) Reject H0 if 2 > 67.5048 D) Reject H0 if 2 > 34.7642

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2 Perform Test of Hypothesis for Population Variance

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

7) A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was 23.243 minutes and the sample standard deviation was 20.40 minutes. It is desired to determine if the population standard deviation exceeds 20 minutes. Calculate the test statistic for this test of hypothesis.

A) 2 = 51 B) 2 = 53.06 C) 2 = 52.02 D) 2 = 58.11 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) An educational testing service designed an achievement test so that the range in student scores would be greater than 300 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 41 students and found that the sample mean and variance were 687 and 2605, respectively. Specify the null and alternative hypotheses for determining whether the test achieved the desired dispersion in scores. Assume that range = 6.

9) An educational testing service designed an achievement test so that the range in student scores would be greater than 420 points. To determine whether the objective was achieved, the testing service gave the test to a random sample of 30 students and found that the sample mean and variance were 759 and 1943, respectively.

Conduct the test for H0: 2 = 4900 vs. Ha: 2 > 4900 using = .025. Assume the range is 6.

10) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .05 to ensure proper inoculation. A random sample of 31 injections resulted in a variance of .103. Specify the rejection region for the test. Use

= .10.

11) A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .07 to ensure proper inoculation. A random sample of 25 injections was measured. Suppose the p-value for the test is p = .0024. State the proper conclusion using = .01.

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Ch. 8 Inferences Based on a Single Sample: Tests of Hypothesis Answer Key

8.1 The Elements of a Test of Hypothesis

1

Write Null and Alternative Hypotheses

1) A

2) A

3) A

4) A

5) C

6) A

7) B

8) To determine if the new method is more accurate in detecting cancer than the old method, we test:

H0: p = .17 vs. Ha: p < .17
9) To determine if the mean yield for the soybeans differs from 594 bushels per acre, we test:
H0: =594 vs. Ha: =594
Interpret Type I and Type II Errors
10) A 11) A 12) A 13) A 14) A 15) A 16) B 17) A 18) A 19) A 20) C 21) D 22) A 23) B 24) B 25) B
2
8.2 Formulating Hypotheses and Setting Up the Rejection Region
1 Identify Rejection Region
1) A 2) A 3) A
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4)
5)
6)
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7)
8)
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9)
10)
11) A
12) A
13) B
14) A
15) A
16) B
8.3 Test of Hypothesis about a Population Mean: Normal (z) Statistic
1 Perform Hypothesis Test for Population Mean
1) A 2) A 3) A 4) A 5) A 6) A 7) B 8) A 9) C
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10) To determine whether the mean time has been

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