How much does a sleeping bag cost? let's say you want a sleeping bag that should keep you warm in temperatures from 20 degrees f to 45 degrees . a random sample of prices for sleeping bags in this temperature range was taken from backpacker magazine: gear guide (vol.25 issue 157, no 2) brand names include american camper, cabela's camp 7, caribou, cascade, and coleman 80,90,100,120,75,37,30,23,100,110 105,95,105,60,110,120,95,90,60,70 a) use a calculator with mean and sample standard deviation keys to verify that sample mean is around $83.75 and s is around $28.97 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. c) what does the confidence interval mean in the context of this problem?

a)

b) The 90% confidence interval would be given by (72.551;94.949)    

c)We are 90% confident that the true mean temperature for the sleeping bags it's between 72.551 and 94.949

Step-by-step explanation:

Data set given

80,90,100,120,75,37,30,23,100,110 105,95,105,60,110,120,95,90,60,70

Part a

We can calculate the sample mean and the sample deviation with the following formulas:

Part b

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,19)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 90% confidence interval would be given by (72.551;94.949)    

Part c

We are 90% confident that the true mean temperature for the sleeping bags it's between 72.551 and 94.949

the answer is 0.071

good luck! : d