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

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1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or Solve the problem. 1. Find forα=0.01. A B C D Whatistheconfidencelevelofthefolowingconfidenceintervalforμ? ± 2.33 A. 67% B. 78% C. 98% D. 233% 3. The registrar's office at State University would like to estimate the average commute time and determine a 95% confidence interval for the average commute time of evening university students from their usual starting point to campus. A member of the staff randomly chooses a parking lot and selects the first 100 evening students who park in the chosen lot starting at 5 PM. The confidence interval is A. not meaningful because the sampling distribution of the sample mean is not normal. B. meaningful because the sample size exceeds 30 and the central limit theorem ensures normality of the sampling distribution of the sample mean. C. not meaningful because of the lack of random sampling. D. meaningful because the sample is representative of the population. 4. Forty-five CEOs from the electronics industry were randomly sampled and a 90% confidence interval for the average salary of all electronics CEOs was constructed. The interval was. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A. Decrease the sample size and increase the confidence level. B. Decrease the sample size and decrease the confidence level. C. Increase the sample size and increase the confidence level. 1

2 D. Increase the sample size and decrease the confidence level. 5. Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 403 of its members at random and monitor their working time for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are hours and hours, find a 95% confidence interval for the true mean number of hours absent per month per employee. A. 8.6 ±. 123 B. 8.6 ±.0 13 C. 8.6 ±. 157 D. 8.6 ± Find the value t o such that the following statement is true: P( -t o t t o ) =.01 where df = 9. A B C D A marketing research company needs to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than A. I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level. B. Yes and I am 97% confident of it. C. Yes and I am 78% confident of it. D. I am 97% confident that the average compensation is $3,000, The increasing cost of health care is an important issue today. Suppose that a random sample of 23 small companies that offer paid health insurance as a benefit was selected. The mean health insurance cost per worker per month was $132, and the standard deviation was $32. Calculate a 95% confidence interval for the mean health cost per worker per month for all small companies. A. 132 ± B. 132 ± C. 132 ± D. 132 ± SHORT ANSWER. Write the word or phrase that best completes each statement or 2

3 9. The U.S. Commission on Crime wishes to estimate the fraction of crimes related to firearms in an area with one of the highest crime rates in the country. The commission randomly selects 600 files of recently committed crimes in the area and finds 380 in which a firearm was reportedly used. Find a 95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or 10. A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98% confident that the margin of error is within 3%? A B C D A math department needs to estimate the average time it takes Statistics I students to finish a computer project to within 2 hours at 98% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval? A. 20 B. 17 C. 115 D. 267 SHORT ANSWER. Write the word or phrase that best completes each statement or 12. Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $300 with 99% reliability. The initial sales indicate the standard deviation of the weekly sales figures to be approximately $1675. How many weeks of data must be sampled for the company to get the information it desires? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or 13. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a interval. A. biased B. wider C. less significant 3

4 D. narrower 14. A revenue department is under orders to reduce the time small business owners spend on filling out pension form ABC Previously the average time spent on the form was 5.1 hours. In order to prove that the time to fill out the form is reduced, a sample of 48 small business owners who annually complete the form is randomly chosen, and their completion times are recorded. The mean completion time for ABC form was 4.7 hours with a standard deviation of 2.9 hours. In order to prove the time to complete the form is reduced, state the appropriate null and alternative hypotheses to test. A. H o :μ 5.1 H a :μ<5.1 D. H o :μ=5.1 H a :μ 5.1 B. H o :μ=5.1 H a :μ>5.1 E. H o :μ>5.1 H a :μ<5.1 C. H o :μ=5.1 H a :μ= The owner of Get-A-Away Travel has recently surveyed a random sample of 357 customers of the agency. He would like to determine whether or not the mean age of the agency's customers is over 35. If so, he plans to alter the destination of their special cruises and tours. If not, no changes will be made. The appropriate hypotheses are H o :μ = 35, H a :μ>35.ifheconcludesthemeanageisover35whenitisnot,hemakesa error. If he concludes the mean age is not over 35 when it is, he makes a error. A. Type II; Type I B. Type II; Type II C. Type I; Type I D. Type I; Type II 16. An insurance company states that their claim office is able to process all death claims within 4 working days. Recently there have been several complaints that it took longer than 4 days to process a claim. Top management wants to make sure that the situation is status quo and 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 4

5 statistical test, it is concluded that the average 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 II error B. Type I error C. Type III error D. No error occurred in the statistical sense. 17. 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 if the average time spent on the deliveries does not exceed 26 minutes. The owner has randomly selected 17 customers and has delivered pizzas to their homes. What are the hypotheses the owner should test to show that the pizza delivery will not be successful? A. H o :μ 26vs.H a :μ<26 B. H o :μ 26vs.H a :μ>26 C. H o :μ=26vs.h a :μ 26 D. H o :μ<26vs.h a :μ= A national organization has been working with utilities throughout the nation to find sites for large wind machines for generating electric power. Wind speeds must average more than 15 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site under construction for a wind machine. Based on a sample of wind speed recordings (taken at random intervals) at the site, the wind speeds averaged with a standard deviation of To determine whether the site meets the organization's requirements, consider the test, where μisthetruemeanwindspedathesiteand 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 15 mph when it actually 15 mph." A. equals; exceeds B. exceeds; equals C. equals; equals D. exceeds; exceeds 19. What is the probability associated with not making a Type II error? A.α B. (1 - β) C.β D. (1 - α) 5

6 20. We never conclude "Accept H o in a test of hypothesis. This is because: A. The rejection region is not known. B.αistheprobabilityofaTypeIeror. C.β=p(TypeIeror) is not known. D. The p-value is not small enough. 21. The value that separates a rejection region from an acceptance region is called a. A. confidence coefficient B. parameter C. critical value D. significance level 22. 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. significance level B. critical value C. parameter D. test statistic 23. A hypothesis test is used to prevent a machine from underfilling or overfilling quart bottles of beer. On the basis of sample, the null hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals there is nothing wrong with the filling machine. From a statistical point of view: A. A Type I error was made. B. A correct decision was made. C. Both Type I and Type II errors were made. D. A Type II error was made. 24. How many tissues should a package of tissues contain? Researchers determined that 55 tissues is the average number of tissues used during a cold. Suppose a random sample of 10,000 tissue users yielded the following data on the number of tissues used during a cold: Using the sample information provided, calculate the value of the test statistic. A. z = B. z = 6

7 C. z = D. z = SHORT ANSWER. Write the word or phrase that best completes each statement or 25. A revenue department is under orders to reduce the time small business owners spend on filling out pension form ABC Previously the average time spent on the form was 70 hours. In order to prove that the time to fill out the form is reduced, a sample of 99 small business owners who annually complete the form is randomly chosen and their completion times are recorded. The mean completion time for ABC form was 69.6 hours with a standard deviation of 29 hours. State the rejection region for the desired test if testing at MULTIPLE CHOICE. Choose the one alternative that best completes the statement or 26. Given Ho: μ 18,H a :μ<18,andp=0.085.doyourejectorfailtorejecth o at the 0.05 level of significance? A. not sufficient information to decide B. reject H o C. fail to reject H o 27.Ifahypothesistestwereconductedusingα=0.10,forwhichofthefollowing p- values would the null hypothesis be rejected. A B C D 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 13 ounces printed on each cartridge. To check this claim, a sample of cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: To determine whether the supplier's claim is true, consider the test, 7

8 whereμisthetruemeanweightofthecartridges.calculatethevalueofthetest statistic. A B C D The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have PC's at home. Find the rejection region for this test using A. Reject if z > 1.96 or z < B. Reject if z < C. Reject if z > D. Reject if z = The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.6. Find the p-value for a twotailed test of hypothesis. A B C D A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of 100 doctors results in 87 who indicate that they recommend brand Z. The test statistic in this problem is approximately: A B C D SHORT ANSWER. Write the word or phrase that best completes each statement or 32. 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 to their workers. A random sample of 300 manufacturing firms is selected, and only 32 of them offer child-care benefits. Specify 8

9 therejectionregionthatheunionwilusewhentestingatα=.10. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or 33. I want to test H o : p =.7 vs. H a :p.7usingatestofhypothesis.thistestwouldbe called a(n) test. A. two-tailed B. one-tailed C. upper-tailed D. lower-tailed 9