9

For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?

**A.**–3.32 **B.**6.69 **C.**3.32 **D.**0.95

**10.**Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that *s*= $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?

**A.**16 **B.**4 **C.**15 **D.**8

**11.**Which of the following statements *correctly*compares the *t*-statistic to the *z*-score when creating a confidence interval?

**A.**You can use *t*all the time, but for *n*? 30 there is no need, because the results are almost identical if you use *t*or *z*. **B.**Using *t*is easier because you do not have to worry about the degrees of freedom, as you do with *z*. **C.**The value of *z*relates to a normal distribution, while the value of *t*relates to a Poisson distribution.

**D.**Use *t*when the sample size is small, and the resulting confidence interval will be narrower.

**12.**What sample size is required from a very large population to estimate a population proportion within 0.05 with 95% confidence? Don't assume any particular value for *p*.

**A.**767 **B.**271 **C.**385 **D.**38

**13.**In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the population mean is somewhere between **A.**65.33 and 95.33. **B.**71.36 and 90.24.

**C.**69.15 and 92.45. **D.**73.36 and 88.24.

**14.**In sampling without replacement from a population of 900, it's found that the standard error of the

mean, *?* is only two-thirds as large as it would have been if the population were

*x*

infinite in size. What is the approximate sample size?

**A.**600 **B.**400 **C.**200 **D.**500

**15.**The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?

**A.***H*0: *p*? 0.10 and *H*1: *p*> 0.10 **B.***H*0: *p*> 0.10 and *H*1: *p*? 0.10

**C.***H*0: *p*= 0.10 and *H*1: *p*? 0.10 **D.***H*0: *p*? 0.10 and *H*1: *p*< 0.10

**16.**To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?

**A.**18.3, 95% **B.**18.3, 0.95 **C.**20.3, 95% **D.**20.3, 0.95

**17.**Nondirectional assertions lead *only*to _______ tests.

**A.**left-tail **B.**two-tail **C.**right-tail **D.**one-tail

**18.**A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use *?*

= 0.05 and assume a normally distributed population.

**A.**Yes, because the sample mean of 9.25 is below 9.5.

**B.**No, because the test statistic is –1.85 and falls in the rejection region.

**C.**No, because the test statistic falls in the acceptance region.

**D.**Yes, because the test statistic is greater than –1.645.

**19.**A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.

**A.**68.72 to 79.68 **B.**64.92 to 83.48

**C.**13.64 to 134.76 **D.**63.14 to 85.26

**20.**What is the purpose of sampling?

**A.**To achieve a more accurate result than can be achieved by survey

**B.**To estimate a target parameter of the population

**C.**To create a point estimator of the population mean or proportion

**D.**To verify that the population is approximately normally distributed