Question

# How much does a sleeping bag cost? Let's say you want a sleeping bag that should...

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.

 110 70 50 55 95 50 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-bar and sample standard deviation s. (Round your answers to two decimal places.)

 x-bar = \$ 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 \$

a)
xabr = 80.15
s = 28.93

b)

sample mean, xbar = 80.15
sample standard deviation, s = 28.93
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 * 28.93/sqrt(20)
ME = 11.2

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (80.15 - 1.729 * 28.93/sqrt(20) , 80.15 + 1.729 * 28.93/sqrt(20))
CI = (68.97 , 91.33)

 lower limit = 68.97 \$ upper limit = 91.33

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