Developing an Understanding of Statistical Concepts The following exercises are what-if analyses designed to determine what happens to the test statistics and interval estimates when elements of the statistical inference change. These problems can be solved manually or using the Do-It-Yourself Excel spreadsheets you created. 12.3 a. A random sample of 25 was drawn from a population. The sample mean and standard deviation are x = 510 and s = 125. Estimate with 95% confidence. b. Repeat part (a) with n = 50. c. Repeat part (a) with n = 100. d. Describe what happens to the confidence interval estimate when the sample size increases.

12.8 a. The sample mean and standard deviation from a sample of 81 observations are x = 63 and s = 8. Estimate with 95% confidence. b. Repeat part (a) with n = 64. c. Repeat part (a) with n = 36. d. Describe what happens to the confidence interval estimate when the sample size decreases.

12.15 A random sample of 8 observations was drawn from a normal population. The sample mean and sample standard deviation are x = 40 and s = 10. a. Estimate the population mean with 95% confidence. b. Repeat part (a) assuming that you know that the population standard deviation is = 10. c. Explain why the interval estimate produced in part (b) is narrower than that in part

12.25 Xr12-25 A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data are listed here. Do these data allow us to infer at the 5% significance level that the doctors claim is true? 16 23 18 41 22 18 23 19 22 15 18 35 16 15 17 19 23 15 16 26

12.68 a. A random sample of 100 observations was drawn from a normal population. The sample variance was calculated to be s 2 = 220. Test with = .05 to determine whether we can infer that the population variance differs from 300. b. Repeat Part a changing the sample size to 50. c. What is the effect of decreasing the sample size?

12.71 Xr12-71 The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are listed here. Estimate the variance of the entire population of cereal box weights with 90% confidence. 1.05 1.03 .98 1.00 .99 .97 1.01 .96

12.74 Xr12-74 During annual checkups physicians routinely send their patients to medical laboratories to have various tests performed. One such test determines the cholesterol level in patients blood. However, not all tests are conducted in the same way. To acquire more information, a man was sent to 10 laboratories and had his cholesterol level measured in each. The results are listed here. Estimate with 95% confidence the variance of these measurements. 188 193 186 184 190 195 187 190 192 196

12.86 Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.

12.87 Suppose that you used the sample size calculated in Exercise 12.86 and found p^ = .5. a. Estimate the population proportion with 90% confidence. b. Is this the result you expected? Explain.