Fall 2016

## Final Exam

1). The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of .04 inch. If many random samples of 16 Ping-Pong balls are selected, *(10pts)*

a). what is the probability that the sample means will be between 1.29 and 1.33 inches?

b). at what diameter will no more than 60% of the sample means be?

c). which is more likely to occur, an individual ball above 1.34 inches, a sample mean above 1.32 inches in a sample size of 4, or a sample mean above 1.31 inches in a sample size of 16? *Explain*

2). A firm that installs large computers has introduced a new training course for installers. The first class of seven has just completed the course. Their scores are 68, 55, 56, 64, 47, 55, and 54. Assuming that these seven people are a random sample of trainees and the scores are normally distributed, find a 96% confidence interval estimate of the mean score for the new training course. *(10pts)*

3). ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. However, if too much cash is unnecessarily kept in the ATMs, the bank is foregoing the opportunity of investing the money and earning interest. Suppose that at a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend has historically been $150 with a population standard deviation of $40. The branch manager selects a random sample of 50 ATM transactions to test whether the population mean withdrawal amount has changed. The mean of the sample was $136.00. Using the 0.10 level of significance, test the claim being made using the critical value approach to hypothesis testing. Also, compute the p-value and interpret its meaning. Explain your conclusion. *(10pts*

4). a). Many Americans who work in large offices also work at home or in the office on weekends. How large a sample should be taken to estimate the population mean amount of time worked on weekends with a sampling error of 10 minutes? Use 95% confidence and assume that the planning value for the population standard deviation is 45 minutes. *(5pts)*

b). A well-known bank credit card firm is interested in estimating the proportion of credit card holders who carry a nonzero balance at the end of the month and incur an interest charge. Assume that the desired sampling error is .03 at 93% confidence. How large a sample should be selected if it is anticipated that roughly 70% of the firm’s cardholders carry a nonzero balance at the end of the month? *(5pts)*

5). A recent article claims that the average supermarket trip is at least 25 minutes. A random sample of 40 shoppers is selected. The study finds a mean of 23.9 minutes with a standard deviation of 8.5 minutes. Test the appropriate hypothesis using the critical value approach with α = 0.06. * *Explain your conclusion. * (10pts)*

6). In a study reported in the Wall Street Journal on April 6, 2009, the Tupperware Corporation surveyed 1,007 U.S. workers. Of the people surveyed, 665 indicated that they take their lunch to work with them. Of these 665 taking their lunch, 200 reported that they carry the lunch in a brown bag. Consider the population of U.S. workers who take their lunch to work with them. Set up a 99% confidence interval estimate of the population proportion that takes brown-bag lunches. *(10pts)*

7). You are a manager of a restaurant that delivers pizza to college dormitory rooms. You have changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard deviation is 6.0 minutes. A sample of 30 orders using the new delivery process yields a sample mean of 22.4 minutes. Using the 0.0089 level of significance, is there evidence that the mean delivery time has been reduced from 25 minutes? Compute the p-value and interpret its meaning. Explain your conclusion rounding your Z-test statistic to (2) decimal places. *(10pts)*

8). Part of a study to determine factors influencing family medical expenses involves finding a regression relationship between the number of people in a family and the monthly medical expense. The data for the pilot study is located in the *MEDICAL* tab in the Excel file provided. *(15 pts)*

a). Develop a regression model at the .05 level of significance.

b). What can be said regarding the slope and correlation coefficient? Conduct the (t)-test for the correlation coefficient.

c). Use your results in (a) to determine the monthly medical expenses for a family of (4)? Is this meaningful?

d). Use your results in (a) to determine the monthly medical expenses for single person household? Is this meaningful?

9). Consider the earnings per share and the closing stock price of selected biotechnical firms with large market capitalization located in the *STOCK* tab in the Excel file provided. Given the importance of many analysts place on earnings per share, you might expect to find a strong correlation between earnings per share and stock price. Of course, it may be premature to judge since the market price may depend more on the expectation of (random) future earnings than on the actual achieved earnings. Use α = .05. *(15 pts)*

a). Draw a scatterplot of the stock price against earnings per share.

b). Determine the coefficient of determination and interpret its meaning.

c). Using α = .05, develop a regression model.

d). You are head of a biotech firm planning to go public soon. Your earnings per share are $.05. Based on your model in (c), what stock price would you anticipate?