In order to determine the average weight of carryon luggage

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of
carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation
of the population to be 8 pounds.
a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

Solution

a) Determine a 97% confidence interval estimate for the mean weight of the carry on luggage. 18 +/- 2.17*7.5/square root of 25 18 +/- 3.2551 Lower limit: 18 – 3.2551 = 14.7449 Upper limit: 18 + 3.2551 = 21.2551 Confidence interval: (14.7449, 21.2551) b) Determine a 95% confidence interval estimate for the mean weight of the carry on luggage. 18 +/- 1.96*7.5/square root of 25 18 +/- 2.9399 Lower limit: 18 – 2.9399 = 15.0601 Upper limit: 18 + 2.9399 = 20.9399 Confidence interval: (15.0601, 20.9399)