Chapter 8.2, Problem 14P

In Problems 13-19. assumethat the population of x values has an approximately normal distribution.

Camping: Cost of a Sleeping Bag How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from $\text{20°F to 45°F}$. A random sample of prices ($) for sleeping bags in this temperature range was taken from Backpacker Magazine: Gear Guide (Vol. 25. Issue 157, No. 2). Brand names include American Camper. Cabela’s. Camp 7. Caribou. Cascade, and Coleman.

80	90	100	120	75	37	30	23	100	no
105	95	105	60	no	120	95	90	60	70

(a) Use a calculator with mean and sample standard deviation keys to verify that $\bar{x}\approx \$83.75\text{ and }s\approx \$28.97$.

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price µ of all summer sleeping bags.

(c) Interpretation What does the confidence interval mean in the context of this problem?