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	50	115	115	40	100	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

The statistical software output for this problem is :

   : Mean of Variable

one sample T cofidence interval :

a ) The mean of the data is :

  

Here n = 20, = 45, 50, 115...........60, 70

  

  

The mean of the data is = 81.9

Standard Deviation :S

  

  

  

b ) Using the t-distribution tables, critical value at 10% level of signifivance with degree of freedom 19 is ,

Substitute the values in the formula of confidence interval :

where

81.9 - 1.729 (31.42 / ) <   < 81.9 + 1.729 (31.42 / )

69.75 <   < 94.05

The 90 % confidence interval for the mean price of all summer bags is (69.75 , 94.05)

=> A 90% confidence interval for the mean price of all summer sleeping bags is,

By using MINITAB, find confidence interval with the help of following steps are :

1) Import the data.

2) Select the start and choose the Basic Statistics option.

3) Select the 1 Sample t and select Samples in coloumns.

4) Click option button choose level of significants and alternative hypothesis.

5) Click ok .

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