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 40 75 80 45 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. Mean value is

Create the following table.

data	data-mean	(data - mean)2
35	-42.9	1840.41
110	32.1	1030.41
40	-37.9	1436.41
75	-2.9	8.41
80	2.1	4.41
45	-32.9	1082.41
30	-47.9	2294.41
23	-54.9	3014.01
100	22.1	488.41
110	32.1	1030.41
105	27.1	734.41
95	17.1	292.41
105	27.1	734.41
60	-17.9	320.41
110	32.1	1030.41
120	42.1	1772.41
95	17.1	292.41
90	12.1	146.41
60	-17.9	320.41
70	-7.9	62.41

Find the sum of numbers in the last column to get.

So standard deviation is

b. Now as n is less than 30 and population standard deviation is not known, so we will use t distribution

TINV(0.1,19)=1.729

So Margin of Error is

So CI is