Question

A company wants to establish that the mean life of its batteries, when used in a wireless mouse, is over 183 days. The data will consist of the life lengths of batteries in 64 different wireless mice.

a) Formulate the null and alternative hypotheses.

b) If the true mean is 190 days, what error can be made?

Answer 1

a) Null and alternative hypotheses are:

`H_(0)`: mu=183 days

`H_(a)`: mu>183 days

b) If the true mean is 190 days, Type II error can be made.

Explanation:

Let mu be the mean life of the batteries of the company when it is used in a wireless mouse

Null and alternative hypotheses are:

`H_(0)`: mu=183 days

`H_(a)`: mu>183 days

Type II error happens if we fail to reject the null hypothesis, when actually the alternative hypothesis is true.

That is if we conclude that mean life of the batteries of the company when it is used in a wireless mouse is at most 183 days, but actually mean life is 190 hours, we make a Type II error.