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Business Analytics (Evans)
Chapter 6 Sampling and Estimation
1) A ________ is a description of the approach that is used to obtain samples from a population prior to any data collection activity.
Answer: C
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO1: Describe the elements of a sampling plan.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
2) Which of the following is true of judgment sampling? A) It selects samples based on expert opinion.
Answer: A
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
3) Which of the following types of sampling involves using random procedures to select a sample?
Answer: B
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
4) ________ involves selecting items from a population so that every subset of a given size has an equal chance of being selected.
Answer: D
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
5) Which of the following sampling methods bases its selection of samples on the ease of data collection?
Answer: D
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
6) Which of the following describes periodic sampling?
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
7) ________ sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset.
Answer: B
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
8) ________ is based on dividing a population into subgroups, sampling a set of subgroups, and conducting a complete census within the subgroups sampled.
Answer: A
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
9) In sampling, ________ involves assessing the value of an unknown population parameter such as a population mean, population proportion, or population varianceusing sample data. A) distribution
Answer: C
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
10) From the standard deviation formula, , identify the estimator.
Answer: A
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
11) A(n) ________ is a single number derived from sample data that is used to estimate the value of a population parameter. A) confidence interval
Answer: D
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
12) For which of the following is the value of the estimator said to be biased?
Answer: A
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
13) Which of the following is true of an unbiased estimator value?
Answer: D
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO1: Explain the importance of unbiased estimators.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
14) Which of the following accurately describes a sampling distribution of the mean?
Diff: 1
Blooms: Remember
Topic: Sampling Distributions
LO1: Define the sampling distribution of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
15) Which of the following is the inherent reason why sampling errors occur?
Answer: B
Diff: 1
Blooms: Understand
Topic: Sampling Error
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
16) ________ are statistical errors that are due to the sample not representing the target population adequately. A) Parallax errors
Answer: C
Diff: 1
Blooms: Understand
Topic: Sampling Error
LO1: Describe the difference between sampling error and nonsampling error.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
17) The means of all possible samples of a fixed size n from some population will form a distribution which is known as the ________.
Answer: B
Diff: 1
Blooms: Remember
Topic: Sampling Error
LO1: Define the sampling distribution of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
18) Which of the following is the equation for calculating the standard error of the mean?
Answer: D
Diff: 1
Blooms: Remember
Topic: Sampling Error
LO1: Calculate the standard error of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
19) Which of the following is implied from the standard error of the mean formula?
Diff: 1
Blooms: Remember
Topic: Sampling Error
LO1: Calculate the standard error of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
20) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than $116?
Answer: C
Diff: 2
Blooms: Apply
AACSB: Analytic Skills
Topic: Sampling Distributions
LO1: Define the sampling distribution of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
21) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. If a soccer team of 11 players were to make the next batch of orders, what would be the standard error of the mean? A) 1.64
Answer: B
Diff: 2
Blooms: Apply
AACSB: Analytic Skills
Topic: Sampling Distributions
LO1: Define the sampling distribution of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
22) The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. If a soccer team of 11 players were to make the next batch of orders, what is the probability that the mean purchase would exceed $116?
Answer: D
Diff: 2
Blooms: Apply
AACSB: Analytic Skills
Topic: Sampling Distributions
LO1: Define the sampling distribution of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
23) ________ states that if the sample size is large enough, the sampling distribution of the mean is approximately normally distributed, regardless of the distribution of the population and that the mean of the sampling distribution will be the same as that of the population.
Answer: B
Diff: 1
Blooms: Remember
Topic: Sampling Distributions
LO1: Explain the practical importance of the central limit theorem.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
24) The central limit theorem states that if the population is normally distributed, then the ________.
Answer: D
Diff: 1
Blooms: Understand
Topic: Sampling Distributions
LO1: Explain the practical importance of the central limit theorem.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
25) Which of the following is a difference between interval estimates and point estimates?
Diff: 2
Blooms: Understand
Topic: Interval Estimates
LO1: Explain how an interval estimate differs from a point estimate.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
26) A ________ is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true population parameter.
Answer: C
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
Answer: B
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
29) The ________ is a family of probability distributions with a shape similar to the standard normal distribution. A) lognormal distribution B) Gaussian qdistribution
Answer: D
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
30) Which of the following is a difference between the tdistribution and the standard normal distribution?
Answer: C
Diff: 2
Blooms: Understand
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
31) Which of the following is true of the tdistribution?
Answer: C
Diff: 2
Blooms: Understand
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
32) Which of the following is true of calculating confidence intervals for larger samples? A) For larger samples, the tdistribution is indistinguishable from the standard normal distribution.
Diff: 2
Blooms: Understand
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
33) Which of the following types of distributions use zvalues to establish confidence intervals? A) Gaussian qdistribution
Answer: D
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
Use the table below to answer the following question(s).
The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the mean volume. The historical standard deviation is 5 milliliters. In filling 250milliliter bottles, a sample of 20 found a meanvolume of 242 milliliters.
Velvetta Inc. Shampoo
Production 

Alpha Value  0.05 
Standard Deviation  5 
Sample Size  20 
Sample Mean  242 
34) Based on the data in the table above, calculate the margin of error at 95% confidence interval. A) 1.84
Answer: B
Diff: 1
Blooms: Apply
AACSB: Analytic Skills
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
35) From the table above, calculate the _{/} value at a 95% confidence interval.
Answer: C
Diff: 1
Blooms: Apply
AACSB: Analytic Skills
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
36) From the table above, determine the cumulative probability for z at a 95% confidence level. A) 0.975
Answer: A
Diff: 1
Blooms: Apply
AACSB: Analytic Skills
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
37) From the table above, calculate the lower confidence interval estimate at a confidence level of 95% A) 239.49
Answer: C
Diff: 1
Blooms: Apply
AACSB: Analytic Skills
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
38) The formula for a 100(1 )% confidence interval for the mean when the population standard deviation is unknown is ________.
Answer: B
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Calculate confidence intervals for population means and proportions using the formulas in the chapter and the appropriate Excel functions.
LO2: Discuss the applications of confidence interval estimation
39) In which of the following cases is a proportion of the observations of a sample used in estimating the confidence interval?
Answer: D
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Use confidence intervals to draw conclusions about population parameters. LO2: Discuss the applications of confidence interval estimation
40) In the equation for calculating a confidence interval for a proportion, p z_{a}_{/2} , what
does represent?
Answer: C
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Use confidence intervals to draw conclusions about population parameters. LO2: Discuss the applications of confidence interval estimation
41) A ________ is one that provides a range for anticipating the value of a new observation from the same population. A) prediction interval
Answer: A
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Compute a prediction interval and explain how it differs from a confidence interval. LO2: Discuss the applications of confidence interval estimation
42) Which of the following is true of prediction intervals?
Answer: B
Diff: 2
Blooms: Understand
Topic: Prediction Intervals
LO1: Compute a prediction interval and explain how it differs from a confidence interval. LO2: Discuss the applications of confidence interval estimation
2
43) Which of the following is true of the equation [n (z_{}_{/2})] for computing the sample
size required to achieve a desired confidence interval halfwidth for a proportion? A) The sample size calculated will only be an approximation.
Answer: D
Diff: 1
Blooms: Understand
Topic: Prediction Intervals
LO1: Compute sample sizes needed to ensure a confidence interval for means and proportions with a specified margin of error.
LO2: Discuss the applications of confidence interval estimation
44) The table below shows the weights of female individuals in Catherines family. Calculate the sample variance in the weights, and the standard deviation.
Weights of female individuals in Catherines
family (in lbs) 
163 
160 
155 
161 
158 
155 
149 
151 
158 
171 
Answer: Sample variance is calculated by the formula, s2 = (1)
Where, n = number of samples
is the sum of individual samples minus the sample mean.
N= 10,
= (163+160+155+161+158+155+149+151+158+171) / 10 = 158.1
Therefore substituting the values in equation (1), and by simplifying the values, we get,
=24.01+3.61+9.61+8.41+.01+9.61+82.81+50.41+.01+166.41 / 9 =354.9 / 9 =39.43.
Therefore, total variance is 39.43.
Standard deviation is the positive square root of variance.
Therefore, standard deviation = = 6.28.
Diff: 2
Blooms: Apply
AACSB: Analytic Skills
Topic: Estimating Population Parameters
LO1: Explain how the average, standard deviation, and distribution of means of samples changes as the sample size increases.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
45) The table below shows the number of goals scored by the Huntington Soccer Club in their league for the past 12 years. Calculate the standard error of the mean of the data given that the variance of the data is 50.45
Goals Scored by the Huntington
Soccer Club for the past 12 years 

Year 1  45 
Year 2  51 
Year 3  33 
Year 4  40 
Year 5  30 
Year 6  38 
Year 7  49 
Year 8  52 
Year 9  46 
Year 10  43 
Year 11  40 
Year 12  50 
Answer: Standard error of the mean is calculated by the formula (1), where is the standard deviation of the data, and n is the number of samples.
Standard deviation is the positive square root of variance, and since we have the variance value as 50.45, the standard deviation is _{ }=7.10 n = 12(2) =7.10(3)
Substituting (2) and (3) in (1), we get 7.10 / = 2.05
Therefore the standard error of the mean = 2.05
Diff: 2
Blooms: Apply
AACSB: Analytic Skills
Topic: Sampling Distributions
LO1: Calculate the standard error of the mean.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
Answer: FALSE
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO2: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.
Answer: TRUE
Diff: 1
Blooms: Remember
Topic: Estimating Population Parameters
LO2: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.
Diff: 1
Blooms: Remember
Topic: Estimating Population Parameters
LO2: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.
Answer: FALSE
Diff: 1
Blooms: Remember
Topic: Sampling Error
LO1: Describe the difference between sampling error and nonsampling error.
LO2: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.
Answer: TRUE
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
Answer: TRUE
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
Answer: FALSE
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
Answer: TRUE
Diff: 1
Blooms: Remember
Topic: Prediction Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
Answer: TRUE
Diff: 1
Blooms: Remember
Topic: Confidence Intervals and Sample Size
LO1: Explain how confidence intervals change as the level of confidence increases or decreases. LO2: Discuss the applications of confidence interval estimation
Answer: Selecting a sample from a continuous manufacturing process can be accomplished in two main ways. First, select a time at random; then select the next n items produced after that time. Second, select n times at random; then select the next item produced after each of these times. The first approach generally ensures that the observations will come from a homogeneous population; however, the second approach might include items from different populations if the characteristics of the process should change over time.
Diff: 1
Blooms: Remember
Topic: Statistical Sampling
LO1: Explain systematic, stratified, and cluster sampling, and sampling from a continuous process.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
56) Give an account of biased and unbiased estimators in sampling methods.
Answer: Statisticians develop many types of estimators, and from a theoretical as well as a practical perspective, it is important that they truly estimate the population parameters they are supposed to estimate. Suppose that we perform an experiment in which we repeatedly sampled from a population and computed a point estimate for a population parameter. Each individual point estimate will vary from the population parameter; however, we would hope that the longterm average (expected value) of all possible point estimates would equal the population parameter. If the expected value of an estimator equals the population parameter it is intended to estimate, the estimator is said to be unbiased. If this is not true, the estimator is called biased and will not provide correct results.
Diff: 1
Blooms: Remember
Topic: Estimating Population Parameters
LO1: Explain the importance of unbiased estimators.
LO2: Explain the fundamentals of sampling methods, experiment designs, and sampling distributions
57) What is a confidence interval in sampling?
Answer: Confidence interval estimates provide a way of assessing the accuracy of a point estimate. A confidence interval is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true (unknown) population parameter. This probability is called the level of confidence, denoted by 1 , where is a number between 0 and 1. The level of confidence is usually expressed as a percent; common values are 90%, 95%, or 99%.
Diff: 1
Blooms: Remember
Topic: Confidence Intervals
LO1: Define and give examples of confidence intervals.
LO2: Discuss the applications of confidence interval estimation
58) Compare between the tdistribution and the standard normal distribution.
Answer: The tdistribution is actually a family of probability distributions with a shape similar to the standard normal distribution. Different tdistributions are distinguished by an additional parameter, degrees of freedom (df). The tdistribution has a larger variance than the standard normal, thus making confidence intervals wider than those obtained from the standard normal distribution, in essence correcting for the uncertainty about the true standard deviation, which is not known. As the number of degrees of freedom increases, the tdistribution converges to the standard normal distribution. When sample sizes get to be as large as 120, the distributions are virtually identical; even for sample sizes as low as 30 to 35, it becomes difficult to distinguish between the two. Thus, for large sample sizes, many people use zvalues to establish confidence intervals even when the standard deviation is unknown.
Diff: 2
Blooms: Remember
Topic: Confidence Intervals
LO1: Describe the difference between the tdistribution and the normal distribution. LO2: Discuss the applications of confidence interval estimation
59) Compare between a prediction interval and a confidence interval.
Answer: A prediction interval is one that provides a range for predicting the value of a new observation from the same population. This is different from a confidence interval, which provides an interval estimate of a population parameter, such as the mean or proportion. A confidence interval is associated with the sampling distribution of a statistic, but a prediction interval is associated with the distribution of the random variable itself.
Diff: 2
Blooms: Remember
Topic: Prediction Intervals
LO1: Compute a prediction interval and explain how it differs from a confidence interval. LO2: Discuss the applications of confidence interval estimation
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