Chapter 11
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WebQuizzing – Ch. 11
Book ISBN-10 0538477490
Book ISBN-13 9780538477499
Author: Gerald Keller
Title: Statistics for Management and Economics
Ed: 9e
# Questions Submitted: 20 Multiple Choice
1. A robust estimator is one that is:
A. unbiased and symmetrical about zero.
B. consistent and is also mound-shaped.
C. efficient and less spread out.
D. not sensitive to moderate nonnormality.
Analysis:
A. Incorrect. A robust estimator is one that is not sensitive to moderate nonnormality.
B. Incorrect. A robust estimator is one that is not sensitive to moderate nonnormality.
C. Incorrect. A robust estimator is one that is not sensitive to moderate nonnormality.
D. Correct. A robust estimator is one that is not sensitive to moderate nonnormality.
ANSWER: D Ref: Section 11.1
2. For statistical inference about the mean of a single population when the population standard
deviation is unknown, the degrees for freedom for the t-distribution equal n-1 because we
lose one degree of freedom by using the:
A. sample mean as an estimate of the population mean.
B. sample standard deviation as an estimate of the population standard deviation.
C. sample proportion as an estimate of the population proportion.
D. sample size as an estimate of the population size.
Analysis:
A. Correct. We lose one degree of freedom by using the sample mean as an estimate of the
population mean.
B. Incorrect. We lose one degree of freedom by using the sample mean as an estimate of the
population mean.
C. Incorrect. We lose one degree of freedom by using the sample mean as an estimate of the
population mean.
D. Incorrect. We lose one degree of freedom by using the sample mean as an estimate of the
population mean.
ANSWER: A Ref: Section 11.1
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3. For a 99% confidence interval of the population mean based on a sample of n = 25 with s =
0.05, the critical value of t is:
A. 2.7969
B. 2.7874
C. 2.4922
D. 2.4851
Analysis:
A. Correct. The critical value of t is 2.7969
B. Incorrect. The critical value of t is 2.7969
C. Incorrect. The critical value of t is 2.7969
D. Incorrect. The critical value of t is 2.7969
ANSWER: A Ref: Section 11.1
4. Researchers determined that 60 Kleenex tissues is the average number of tissues used during
a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the
number of tissues used during a cold: x = 52 and s = 22. Suppose the test statistic does not
fall in the rejection region at  = 0.05. Which of the following conclusions is correct?
A. At  = 0.05, we do not reject H o .
B. At  = 0.05, we reject H o .
C. At  = 0.05, we accept H o .
D. Both a and c.
Analysis:
A. Correct. At  = 0.05, we do not reject H o is correct.
B. Incorrect. At  = 0.05, we do not reject H o is correct.
C. Incorrect. At  = 0.05, we do not reject H o is correct.
D. Incorrect. At  = 0.05, we do not reject H o is correct.
ANSWER: A Ref: Section 11.1
5. The degrees of freedom for the test statistic for  when  is unknown is:
A. 1
B. n
C. n-1
D. None of these choices.
Analysis:
A. Incorrect. The degrees of freedom for the test statistic for  when  is unknown is n-1
B. Incorrect. The degrees of freedom for the test statistic for  when  is unknown is n-1
C. Correct. The degrees of freedom for the test statistic for  when  is unknown is n-1
D. Incorrect. The degrees of freedom for the test statistic for  when  is unknown is n-1
ANSWER: C Ref: Section 11.1
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6. Based on sample data, the 90% confidence interval limits for the population mean are LCL =
170.86 and UCL = 195.42. If the 10% level of significance were used in testing the
hypotheses H 0 :   201 vs. H1 :   201 , the null hypothesis:
A. would be rejected.
B. would be accepted.
C. would fail to be rejected.
D. would become Ho :   201.
Analysis:
A. Correct. The null hypothesis would be rejected.
B. Incorrect. The null hypothesis would be rejected.
C. Incorrect. The null hypothesis would be rejected.
D. Incorrect. The null hypothesis would be rejected.
ANSWER: A Ref: Section 11.1
7. The statistic (n  1) s 2 /  2 has a chi-squared distribution with n-1 degrees of freedom if:
A. the population is normally distributed with variance equal to  2 .
B. the sample is normally distributed with variance equal to s 2 .
C. the sample has a Student t distribution with degrees of freedom equal to n-1.
D. All of these choices are true.
Analysis:
A. Correct. If the population is normally distributed with variance equal to  2 .
B. Incorrect. If the population is normally distributed with variance equal to  2 .
C. Incorrect. If the population is normally distributed with variance equal to  2 .
D. Incorrect. If the population is normally distributed with variance equal to  2 .
ANSWER: A Ref: Section 11.1
8. Which of the following is not an example illustrating the use of variance?
A. As a measure of risk.
B. As a judge of consistency.
C. To search for and reduce variability in a process.
D. All of these choices are true.
Analysis:
A. Incorrect. All of these choices are true.
B. Incorrect. All of these choices are true.
C. Incorrect. All of these choices are true.
D. Correct. All of these choices are true.
ANSWER: D Ref: Section 11.1
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9. Which of the following conditions is needed regarding the chi-squared test statistic for the
test of variance?
A. The population random variable must be normal.
B. The test statistic must be a non-negative number.
C. The test statistic must have a chi-squared distribution with n-1 degrees of freedom.
D. All of these choices are true.
Analysis:
A. Incorrect. All of these choices are true.
B. Incorrect. All of these choices are true.
C. Incorrect. All of these choices are true.
D. Correct. All of these choices are true.
ANSWER: D Ref: Section 11.1
10. Under what condition(s) does the test statistic for p have an approximate normal distribution?
A. When np > 5.
B. When np and np(1-p) are both > 5.
C. When n > 30.
D. When np and n(1-p) are both > 5.
Analysis:
A. Incorrect. When np and n(1-p) are both > 5
B. Incorrect. When np and n(1-p) are both > 5
C. Incorrect. When np and n(1-p) are both > 5
D. Correct. When np and n(1-p) are both > 5
ANSWER: D Ref: Section 11.2 - 11.3
11. In selecting the sample size to estimate the population proportion p, if we have no knowledge
of even the approximate values of the sample proportion p̂ , we:
A. take another sample and estimate p̂ .
B. take two more samples and find the average of their p̂ .
C. let p̂ =0.50.
D. let p̂ =0.95.
Analysis:
A. Incorrect. We let p̂ =0.50 if we have no knowledge of even the approximate values.
B. Incorrect. We let p̂ =0.50 if we have no knowledge of even the approximate values.
C. Correct. We let p̂ =0.50 if we have no knowledge of even the approximate values.
D. Incorrect. We let p̂ =0.50 if we have no knowledge of even the approximate values.
ANSWER: C Ref: Section 11.2 - 11.3
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12. The use of the standard normal distribution for constructing confidence interval estimate for
the population proportion p requires:
A. npˆ and n(1  pˆ ) both greater than 5.
B. np and n(1-p) both greater than 5.
C. n(1+ p̂ ) and n(1- p̂ ) both greater than 5.
D. sample size greater than 5.
Analysis:
A. Correct. It requires npˆ and n(1  pˆ ) both greater than 5
B. Incorrect. It requires npˆ and n(1  pˆ ) both greater than 5
C. Incorrect. It requires npˆ and n(1  pˆ ) both greater than 5
D. Incorrect. It requires npˆ and n(1  pˆ ) both greater than 5
ANSWER: A Ref: Section 11.2 - 11.3
13. Assuming that all necessary conditions are met, what needs to be changed in the formula
pˆ  t pˆ (1  pˆ ) / n so that we can use it to construct a (1-) confidence interval estimate for the
population proportion p?
A. p̂ should be replaced by p.
B. t should be replaced by z .
C. t should be replaced by t / 2 .
D. t should be replaced by z / 2 .
Analysis:
A. Incorrect. t should be replaced by z / 2 .
B. Incorrect. t should be replaced by z / 2 .
C. Incorrect. t should be replaced by z / 2 .
D. Correct. t should be replaced by z / 2 .
ANSWER: D Ref: Section 11.2 - 11.3
14. The width of a confidence interval estimate for a proportion will be:
A. narrower for 99% confidence than for 95% confidence.
B. wider for a sample size of 100 than for a sample size of 50.
C. narrower for 90% confidence than for 95% confidence.
D. narrower when the sample proportion if 0.50 than when the sample proportion is 0.20.
Analysis:
A. Incorrect. Narrower for 90% confidence than for 95% confidence.
B. Incorrect. Narrower for 90% confidence than for 95% confidence.
C. Correct. Narrower for 90% confidence than for 95% confidence.
D. Incorrect. Narrower for 90% confidence than for 95% confidence.
ANSWER: C Ref: Section 11.2 - 11.3
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15. When determining the sample size needed for a proportion for a given level of confidence
and sampling error, the closer to 0.50 that p is estimated to be:
A. the smaller the sample size required.
B. the larger the sample size required.
C. the sample size is not affected.
D. the effect cannot be determined from the information given.
Analysis:
A. Incorrect. The closer to 0.50 that p is estimated to be the larger the sample size required.
B. Correct. The closer to 0.50 that p is estimated to be the larger the sample size required.
C. Incorrect. The closer to 0.50 that p is estimated to be the larger the sample size required.
D. Incorrect. The closer to 0.50 that p is estimated to be the larger the sample size required.
ANSWER: B Ref: Section 11.2 - 11.3
16. Which of the following would be an appropriate null hypothesis?
A. The population proportion is equal to 0.60.
B. The sample proportion is equal to 0.60.
C. The population proportion is not equal to 0.60.
D. All of these choices are true.
Analysis:
A. Correct. The population proportion is equal to 0.60 would be an appropriate null hypothesis.
B. Incorrect. The population proportion is equal to 0.60 would be an appropriate null hypothesis.
C. Incorrect. The population proportion is equal to 0.60 would be an appropriate null hypothesis.
D. Incorrect. The population proportion is equal to 0.60 would be an appropriate null hypothesis.
ANSWER: A Ref: Section 11.2 - 11.3
17. Which of the following would be an appropriate alternative hypothesis?
A. The population proportion is less than 0.65.
B. The sample proportion is less than 0.65.
C. The population proportion is equal to 0.65.
D. The sample proportion is equal to 0.65.
Analysis:
A. Correct. The population proportion is less than 0.65 would be an appropriate alternative
hypothesis.
B. Incorrect. The population proportion is less than 0.65 would be an appropriate alternative
hypothesis.
C. Incorrect. The population proportion is less than 0.65 would be an appropriate alternative
hypothesis.
D. Incorrect. The population proportion is less than 0.65 would be an appropriate alternative
hypothesis.
ANSWER: A Ref: Section 11.2 - 11.3