A Single Population Mean using the Student t Distribution · Exercise 35

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

(a) (a) $\bar{x}$ = __________
(b) $s_x$ = __________
(c) n = __________
(d) n-1 = __________
(b) Define the random variables $X$ and $\bar{X}$ in words.
(c) Which distribution should you use for this problem? Explain your choice.
(d) Construct a 95% confidence interval for the population mean worth of coupons.
(a) State the confidence interval.
(b) Sketch the graph.
(c) Calculate the error bound.
(e) If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §8.2 A Single Population Mean using the Student t Distribution · Exercise 35