Question

A cell phone company is proposing to offer a discount to seniors if there was evidence that their average call length was less than the overall population mean of 9.2 minutes. If the phone calls are too long and the discount is provided, the company will lose money. A random sample of the length of calls for 100 randomly selected seniors was determined.

(a) State the null and alternative hypotheses. Write 's' as '<=', '' as '>=', and '#' as '<>'.
(b) In context, explain what the Type I error is.
(c) In context, explain what the Type II error is.
(d) Which is worse for the seniors, a Type I error or a Type II error? Why?

Answer 1

Explanation:

1. Null hypothesis:

h0: μ ≥ 9.2

alternative hypothesis

h1: μ < 9.2

2. the type 1 error is an error that occurs when we reject a true null hypothesis. in this question, the type 1 error is commited if we reject the null hypothesis that the population mean is greater than or equal to 9.2, then we have committed this error.

3. the type ll error is an error that o a false occures wehn we do not reject a false null hypothesis. We commit the type ll error in this scenario by saying that the population mean is greater than or less than 9.2 when it is actually false.

4. The type ii eror is actually worse here. we accept a false H0 in the type ii error which says that the mean is greater than or equal to 9.2. This means that these seniors are not going to get discount because they only get discount when their mean calls is less than 9.2 minutes.