Question

ppose we are testing a new shampoo to see if it makes hair grow faster. We knowthat the average rate of hair growth is 0.5 inches per month. The hypothesis are as follows:H0:m0:5vs.H1:m>0:5. Suppose that the null hypothesis is not rejected and that thereal truth is that the shampoo actually does make hair grow faster. What type of error, if any,occurred?

Answer 1

Type II error occurred

Explanation:

It is given that a new shampoo is being tested to determine whether the hair grows faster by using this shampoo.

It is known that hair grow at 0.5 inches per month at average.

The hypothesis are,

Null hypothesis,
`$H_0: \mu=0.5$`

Alternate hypothesis,
`$H_1: \mu>0.5$`

But it is known that :

Type
`$I$` error occurs when rejecting the null hypothesis when the null hypothesis is true actually.

Type
`$II$` error occurs
`\text{when we fail reject the null hypothesis}` when the null hypothesis is actually false.

Now here since the null hypothesis is not been rejected, type
`$II$` error had occurred.