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 35 90 35 65 105 30 23 100 110
105 95 105 60 110 120 95 90 60 70

(a)
(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 four 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 of all summer sleeping bags. (Round your answers to two decimal places.)

lower limit: $
upper limit: $

Answer 1

a) Sample Mean = 79.4

Sample standard deviation = 30.62

b) 90% Confidence interval: (67.56 ,91.24)

Step-by-step explanation:

We are given the following in the question:

Prices for sleeping bags has an approximately normal distribution.

We are given the following sample:

35, 85, 105, 40, 100, 50, 30, 23, 100, 110, 105, 95, 105, 60, 110, 120, 95, 90, 60, 70

a)

Formula:

where are data points, is the mean and n is the number of observations.

Sum of squares of differences = 1971.36 + 31.36 + 655.36 + 1552.36 + 424.36 + 864.36 + 2440.36 + 3180.96 + 424.36 + 936.36 + 655.36 + 243.36 + 655.36 + 376.36 + 936.36 + 1648.36 + 243.36 + 112.36 + 376.36 + 88.36 = 17816.8

b) 90% Confidence interval:

Putting the values, we get,