Question

In order to determine the average weight of carry on luggage by passengers in airplanes, a sample of 225 peices of carry on luggage was collected and weighed. The average weight was 14 pounds. Assume that we know the standard deviation of the population to be 3.5 pounds.

1. determine a 95% confidence interval estimate for the mean weight of carry on luggage?

2. Explain how you know whether to use z or t values in these types of problems.

please give me step by step instructions so I understand how to do this. Thank You.

Answer 1

1. The equation for confidence interval is as follows:

Where Xbar = 14

Z = 1.96 (because confidence interval is 95% i.e. 2.5% is the signifcance level on either side of the normal distribution)

S = Sigma = 3.5

N = sample size = 225

2. We need to use Z because both the following criteria are satisfied:

a) the sample size is greater than 30

b) We know the population variance or standard deviation

If either of the two was not satisfied, we have to use t test.

Refer the figure below: (only for reference)