Question

1. In a random sample of 60 refrigerators, the mean repair cost was $150. Assume thepopulation standard deviation σ = $15.5.

a. Construct a 99% confidence interval for the population mean repair cost. Interpret the results.

b. Repeat exercise 3(a), changing the sample size to n = 40. Which confidence interval is wider? Explain?

c. Repeat exercise 3(a), using a population standard deviation of σ = $19.5. Whichconfidence interval is wider? Explain?

Answer 1

a) From standard normal tables, we have:
P(-2.576 < Z < 2.576) = 0.99

Therefore the confidence interval here is obtained as:

This is the required 99% confidence interval here.

b) For a sample size of 40 instead of 60, the confidence interval is obtained here as:

This is the required 99% confidence interval here. Clearly the confidence interval is wider for a smaller sample size.

c) For a standard deviation of 19.5

Clearly this is a wider confidence interval than 3a) as the standard deviation is higher here.