# STAT 200 Week 5 HomeWork

5. When you construct a 95% confidence interval, what are you 95% confident about?

8. What is the effect of sample size on the width of a confidence interval?

11. A population is known to be normally distributed with a standard deviation of 2.8.

Compute the 95% confidence interval on the mean based on the following sample of nine:

8, 9, 10, 13, 14, 16, 17, 20, 21.

15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean? (b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was 8 hours with a sample standard deviation of 4 hours. Construct a 95% confidence interval for the population mean time wasted.

112. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal. Construct a 95% confidence interval for the population mean cost of a used car.

122. Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eightyear period. Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.