1. All the Questions Must Be Answered. All Questions Carry Equal Points

Homework 7

1. All the questions must be answered. All questions carry equal points. 2. Show the steps in your approach as you arrive at the final solution. Submitting only the answer is not sufficient to get credit.

1. A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the number of patients seen per day is less than 10? Use α = .025 level of significance. What is your conclusion using p-value and critical value approaches. Is the conclusion different in both the cases?

2. At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed. a) State the hypotheses. b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean 935? c) Use the confidence interval approach to conduct a hypothesis test. What is your conclusion? d) Assuming α = .05, conduct p-value based and critical-value based hypothesis tests. How do the results compare in all the three cases?

3. The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out? Use α = .05 level of significance. Use both p-value and critical value approaches. Compare the test results.

4. The following data were collected on the number of emergency ambulance calls for an urban county and a rural county in Florida. Is County type independent of the day of the week in receiving the emergency ambulance calls? Use α = 0.005. What is your conclusion? Day of the Week Sun Mon Tue Wed Thu Fri Sat County Urban 62 47 48 51 61 74 41 Rural 6 10 18 17 11 13 12

5. Medical tests were conducted to learn about drug-resistant tuberculosis. Of 284 cases tested in New Jersey, 18 were found to be drugresistant. Of 536 cases tested in Texas, 10 were found to be drugresistant. Do these data indicate that New Jersey has a statistically significant higher outbreak of drugresistant tuberculosis cases? Use a .03 level of significance. What is the p- value, and what is your conclusion? Is the conclusion any different under critical-value approach?

6. Consider the following data for two independent random samples taken from two normal populations. Sample 1 14 26 20 16 14 18 Sample 2 18 16 8 12 16 14 a) Compute the two sample means and the two sample standard deviations. b) What is the point estimate of the difference between the two population means? c) Assuming α = .10, conduct p-value based and critical-value based hypothesis tests for the equality of means of the two populations. d) What is the 90% confidence interval estimate of the difference between the two population means? How do the results compare in all the three approaches to hypothesis testing?

Homework #8 Chapter 10 1. The Professional Golf Association (PGA) measured the putting accuracy of professional golfers playing on the PGA Tour and the best amateur golfers playing in the World Amateur Championship. A sample of 1800 6-foot putts by amateur golfers found 1044 made putts. A sample of 1700 6-foot putts by professional golfers found 1088 made puts. a. Estimate the proportion of made 6-foot putts by professional golfers. Estimate the proportion of made 6-foot putts by amateur golfers. Which group had a better putting accuracy? b. What is the point estimate of the difference between the proportions of the two populations? What does this estimate tell you about the percentage of putts made by the two groups of golfers? c. What is the 97% confidence interval for the difference between the two population proportions? Interpret his confidence interval in terms of the percentage of putts made by the two groups of golfers. 2. A May 1993 New York Times/CBS News poll found that of 500 adults who were planning a vacation in the next six months, 85 were expecting to travel by airplane. A similar survey question in a 2003 New York Times/CBS News poll sampled 700 adults who were planning a vacation during the next six months and found that 189 were expecting to travel by airplane. a. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period. b. What is the sample proportion expecting to travel by airplane in 2003? In 1993? c. Use α = .06 and test for a significant difference. What is your conclusion? d. Discuss reasons that might provide an explanation for this conclusion. 2 Chapter 11 3. Find the following chi-square distribution values. a. χ 2 0.005 with Sample Size = 101 b. χ 2 0.10 with Sample Size = 30 c. χ 2 0.05 with Sample Size = 16 d. χ 2 0.995 with Sample Size = 19 e. χ 2 0.99 with Sample Size = 96 4. A sample of 27 items provides a sample standard deviation of 10. Test the following hypotheses using α = .10. What is your conclusion? Use both the p-value approach and the critical value approach. H0: σ 2 ≤ 75 Ha: σ 2 > 75 5. The daily car rental rates for a sample of eight cities follow. a. What is the 98% confidence interval estimate of the variance of car rental rates for the population? b. What is the 99% confidence interval estimate of the standard deviation for the population? 3 6. At the end of 2008, the variance in the semiannual yields of overseas government bond was σ 2 = 0.25. A group of bond investors met at that time to discuss future trends in overseas bond yields. Some expected the variability in overseas bond yields to increase and others took the opposite view. The following table shows the semiannual yields for 12 overseas countries as of March 6, 2009. a. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 6, 2009. b. Develop hypotheses to test whether the sample data indicate that the variance in bond yields has increased from that at the end of 2008. c. Use α = .025 to conduct the hypothesis test formulated in part (b). What is your conclusion? 7. Find the critical values based on F distribution when variance of sample 1 is greater than variance of sample 2. Alpha and Sample Sizes are given below. a. α = .05 with n1 = 6 and n2 = 11 b. α = .025 with n1 = 21 and n2 = 26 c. α = .01 with n1 = 61 and n2 = 61 d. α = .10 with n1 = 9 and n2 = 25 4 8. The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a .02 level of significance. What is your conclusion? Which machine of the two provides the greater opportunity for quality improvements? 9. Fidelity Magellan is a large cap growth mutual fund and Fidelity Small Cap Stock is a small cap growth mutual fund. For Fidelity Magellan, the sample standard deviation is 18.89; for Fidelity Small Cap Stock, the sample standard deviation is 13.03. The standard deviation for both funds was computed based on a sample of sizes 26 and 25 respectively. Financial analysts often use the standard deviation as a measure of risk. Conduct a hypothesis test to determine whether the large cap growth fund is riskier than the smaller cap growth fund. Use α = .10 as the level of significance. 3.46 Homework #9 1. Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets. The other category included outlets such as Target, Kmart, and Sears as well as numerous smaller specialty outlets. No individual outlet in this group accounted for more than 5% of the women shoppers. A recent survey using a sample of 200 women shoppers in Tampa, Florida, found 60 Wal-Mart, 29 traditional department store, 11 JC Penney, 14 Kohl’s, 30 mail order, and 56 other outlet shoppers. Does this sample suggest that women shoppers in Tampa differ from the preferences expressed in the U.S. Shopper Data-base? What is your conclusion based on both the p-value and critical-value approaches? Use α = .01. Outlet Percentage Other 35 Wal-Mart 25 Department Stores 10 Mail Order 15 Kohl's 10 J.C. Penney 5 2. The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 largest U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re-investment of dividends. Ratings are assigned by dividing all 1000 largest U.S. companies into four groups of equal size Group A (top rating), B (second best rating), C (third best rating), and D (bottom most rating). Shown here are the one- year ratings for a sample of 50 largest U.S. companies. Does the sample data provide evidence that the ratings are equally likely for the largest U.S. companies? Use α = .025. A B C D 22 9 14 5 3. With double- digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage. The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data is reported as follows: Health Insurance Size of Company Yes No Total Small 50 25 75 Medium 80 20 100 Large 115 10 125 Total 245 55 300 a. Conduct a test of independence using critical value approach to determine whether employee health insurance coverage is independent of the size of the company. Use α = .005. b. What is the p- value, and what is your conclusion? c. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion. 4. FlightStats, Inc., collects data on the number of flights scheduled and the number of flights flown at major airports throughout the United States. FlightStats data showed 56% of flights scheduled at Newark, La Guardia, and Kennedy airports were flown during a three-day snowstorm. All airlines say they always operate within set safety parameters— if conditions are too poor, they don’t fly. The following data show a sample of 600 scheduled flights during the snowstorm. Use the chi- square test with a .10 level of significance to determine whether or not flying/ not flying in a snowstorm is independent of Airliner. What is your conclusion based on Critical Value test? Is it any different from conclusion based on a p-value approach? Flight American Continental Delta United Yes 70 105 95 45 No 80 55 85 65 5. The number of incoming phone calls defined by a Random Variable X at a company switchboard during 1- minute intervals is believed to have a Poisson distribution. Use a .05 level of significance and the following data to test the assumption that the incoming phone calls follow a Poisson distribution. x Observed Freq. 0 14 1 33 2 48 3 44 4 30 5 15 6 9 7 6 8 1