Question: Miles on a Cavalier A researcher is interested in ap­proximating the mean number of miles on three-year­ old Chevy Cavaliers. She finds a random sample of 35 Cavaliers in the Orlando, Florida area and obtains the following results:

37815 20000 57103 46585 24822 49678 30983 52969 8000 39862 6000 65192 34285 30906 41841 39851 43000 74361 52664 33587 52896 45280 30000 41713 76315 22442 45301 52899 41526 28381 55163 51812 36500 31947 16529

a. Obtain a point estimate of the population mean number of miles on a three-year-old Cavalier.
b. Construct and interpret a 99% confidence interval for the population mean number of miles on a three-year-old Cavalier. Assume that σ = 16,100.
c. Construct and interpret a 95% confidence interval for the population mean number of miles on a three-year-old Cavalier. Assume that σ = 16,100.
d. What effect does decreasing the level of confidence have on the width of the interval?
e. Do the confidence intervals computed in parts (b) and (c) represent an interval estimate for the popu­lation mean number of miles on Cavaliers in the United States? Why?
f. How many cars should be in a sample in order to estimate the mean number of miles within 2000 miles with 98% confidence, assuming that σ = 16,100?
g. How many cars should be in a sample in order to estimate the mean number of miles within 1000 miles with 98% confidence, assuming that σ = 16,100?
h. What effect does increasing the required accuracy have on the sample size? Why is this the expected result?