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. 45 100 115 55 85 120 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)

mean = x = 84.65

standard deviation = s = 29.84

b)

sample mean 'x̄=	84.65
sample size   n=	20
sample std deviation s=	29.839
std error 'sx=s/√n=	6.6721
for 90% CI; and 19 df, value of t=		1.729132812
margin of error E=t*std error    =		11.53697089
lower bound=sample mean-E =		73.11302911
Upper bound=sample mean+E =		96.18697089
from above 90% confidence interval for population mean =(73.1130,96.1869)

Lower limit = 73.11

Upper limit = 96.19