After listening to one too many complaints from your daughter about how long you

Question

After listening to one too many complaints from your daughter about how long your son takes in the shower in their shared bathroom you decide to perform a hypothesis test on her belief that he spends more time in the shower on average than she does. You collect a simple random sample of 31 dates and conclude that, at alpha = 0.05, your daughter is correct – that his mean shower length is longer than hers.(Neither child is impressed and both make you promise never to mention hypothesis tests around their friends.)Further, suppose that the true mean shower length of your daughter is actually longer than that of your son.Which of the following is true?

a) You made a type I error

b) You made a type II error

c) You made both type I AND type II errors

d) You made no error

Explanation / Answer

Here we have done Hypothesis testing

where Null Hypothesis : H0 : Mean bathing time for daughter ( d) is equal or more than Mean bathing time for son ( s).

Alternative Hypothesis : H1 : Mean bathing time for son is greater than Mean bathing time for daughter

Here the result is d < s

A type I error is the incorrect rejection of a true null hypothesis so here we can see in this case we have rejected the null hypothesis even it was true so it is a case of type I error.

A type II error is the failure to reject a false null hypothesis so here we can see that we have rejected the null hypothesis so that means it is not a case of type II error.

So, the given case is a Type I error.

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