Question

6. Solve the following problems. Be sure to make a complete statement connecting the confidence interval to the population parameter or the sample size to the margin of error.

a) A study of 40 English composition professors showed that they spent, on average, 12.6 minutes correcting a student’s term paper. Find the 90% confidence interval of the mean time for all English professors when σ = 2.5 minutes.

b) A study of 36 marathon runners showed that they could run at an average rate of 7.8 miles per hour. The sample standard deviation is 0.6 mph. Find the 90% confidence interval for the mean of all runners.

c) A pizza shop wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.15. A previous study showed that the standard deviation of the price was $0.26.

d) A survey of 50 first-time white-water canoers showed that 23 did not want to repeat the experience. Find the 98% confidence interval of the true proportion of canoers who did not wish to canoe the rapids a second time.

e) A recent study indicated that 29% of the 100 women over age 55 in the study were widows.

(i) How large a sample must one take to be 95% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows? (ii) If no estimate of the sample proportion is available, how large should the sample be?

Answer 1

a) Let denotes the mean time for all English professors.

b) Let denotes the mean of all runners.

c)

d) Let p denotes the true proportion who did not want to repeat the experience.