Question

At a carpet store, the mean amount of carpet installed in a residential home is 1250 square feet. It is believed when there is a sale in the store, customers’ purchase of carpeting will increase. A random sample of 45 carpet purchases during a store sale has a sample mean of ¯x. Assume ? = 155 square feet and ? = 0.01. Find the probability of a type II error (ie. not rejecting H₀ when it is in fact not true) if the true mean square footage during a sale is 1330. You may assume normality if needed.

Answer 1

Hypotheses are:

Here we have

The critical value of z for is 2.33. The critical value of sample mean for which we will reject the null hypothesis:

The z-score for and is

The type II error is: