Question

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

90	45	85	110	55	35	30	23	100	110
105	95	105	60	110	120	95	90	60	70

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

x =	$
s =	$

(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. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Answer 1

a)

sample mean, xbar = 79.65
sample standard deviation, s = 30.04

b)

sample size, n = 20
degrees of freedom, df = n - 1 = 19

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.729

ME = tc * s/sqrt(n)
ME = 1.729 * 30.04/sqrt(20)
ME = 11.614

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (79.65 - 1.729 * 30.04/sqrt(20) , 79.65 + 1.729 * 30.04/sqrt(20))
CI = (68.04 , 91.26)

lower limit = 68.04     $
upper limit = 91.26    $