Question

1.

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.

70	55	85	75	70	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) 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.)

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
	70	4900
	55	3025
	85	7225
	75	5625
	70	4900
	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 =	1563	137229

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

(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.)

The provided sample mean is 78.15 and the sample standard deviation is s = 28.173. The size of the sample is n = 20 and the required confidence level is 90%.

The number of degrees of freedom are df = 20 - 1 = 19, and the significance level is α=0.1.

Based on the provided information, the critical t-value for α=0.1 and df = 19 degrees of freedom is t_c = 1.729

The 90% confidence for the population mean \muμ is computed using the following expression

Therefore, based on the information provided, the 90 % confidence for the population mean is

which completes the calculation.