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.

35	110	65	90	90	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

Let X denote the prices ($) for sleeping bags

The sample size is n = 20. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	5	25
	110	12100
	65	4225
	90	8100
	90	8100
	35	1225
	30	900
	23	529
	100	10000
	110	12100
	105	11025
	95	9025
	105	11025
	60	3600
	110	12100
	120	14400
	95	9025
	90	8100
	60	3600
	70	4900
Sum =	1568	144104

The sample mean is computed as follows:

mean = $ 78.4

Also, the sample variance is

Therefore, the sample standard deviation s is

s = $ 33.382

We need to construct the90% confidence interval for the population mean . The following information is provided:

Sample Mean	78.4
Population Standard Deviation	333.382
Sample Size (N)	20

The critical value for is . The corresponding confidence interval is computed as shown below:

CI = ( −44.22 , 201.02 )​

Therefore, based on the data provided, the 90% confidence interval for the population mean is -44.22 < < 201.02, which indicates that we are 90% confident that the true population mean is contained by the interval (-44.2, 201.02).

lower limit = $ -44.22

upper limit = $ 201.02

In case of cost the correct answer may be 0 also, for the lower limit. Since the cost can not be negative