Chapter 6: Statistical Inference.

1. What can you calculate using Excel's functions NORMSINV and NORMSDIST?

2. Suppose that you are conducting a survey on the cost of a medical procedure as part of research on health care reform. The cost of the procedure follows the normal distribution with a standard deviation of 1000. After sampling 50 different hospitals at random, you calculate the average cost to be $5,500. What is the 90% confidence interval for the value of the mean cost of all hospitals? Explain your answer.

3. You work at a plant that manufactures resistors. Previous studies have shown that the number of defective resistors in a batch follows a normal distribution with a mean of 50 and a standard deviation of 15. A new process has been proposed that will reduce the number of defective resistors, saving the plant money. You put the process in place and create a sample of 25 batches. The average number of defects in a batch is 45. Does this prove that the new process reduces the number of defective resistors, or is 45 simply a random aberration, and the process does not make any difference at all? Explain.

4. Who was William Gosset. Where did he work. Why do we care about him?

5. The college administration claims that students should not expect to spend more than an average $200 each semester for books. A student associated with the school newspaper decides to investigate this claim and interviews 25 randomly selected students. The average spent by the 25 students is $200, and the standard deviation of these purchases is $50. Is this significant evidence that the statement from the administration is wrong? Explain.

6. The Excel workbook WLabor.xls contains data on the percentage of women in the work force in 1968 and 1972 taken from a sample of 19 cities. There are two observations from each city, and the observations constitute paired data. You've been asked to determine whether this sample of 19 cities demonstrates a statistically significant increase in the percentage of women in the work force. What is your conclusion. Explain. A government spokesman, viewing some other data on this topic, claims that the percentage of women in the work force has increased 5 points from 1968 to 1972. Does your data conflict with this statement? Explain your answer.

7. To the example above we want to apply a nonparametric test. What nonparametric tests does Excel provide? Does StatPlus add any to those? What's your conclusion if you apply the Wilcoxon Signed Rank test to the work force data? Explain your conclusion.

8. When is the Sign test more effective than the t-test or the signed rank test? Can you apply it to the work force data? Explain.

9. The Excel workbook NurseHome.xls contains data on a random sample of nursing homes collected by the Department of Health and Social Services in new Mexico. You've been asked to examine the data and determine whether there is a difference in revenue generated by rural and non-rural nursing homes. Your conclusions will be used in forming the department's budget for the next year. What are your conclusions. Please explain.