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.

 55 105 110 115 100 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 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 \$

Solution:

Part a

Xbar = 85.40

S = 29.33

(by using calculator or excel)

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 85.4

S = 29.32647448

n = 20

df = n – 1 = 19

Confidence level = 90%

Critical t value = 1.7291

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 85.4 ± 1.7291*29.32647448/sqrt(20)

Confidence interval = 85.4 ± 11.3390

Lower limit = 85.4 - 11.3390 = 74.06

Upper limit = 85.4 + 11.3390 = 96.74

Lower limit = 74.06

Upper limit = 96.74

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