Question

Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, μ , is different from 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 42 hours and that the standard deviation is 4 hours.

What are the null hypothesis ( H0) and the alternative hypothesis (H1) that should be used for the test?

H0:μis ?less than, less than or equal to, greater than, greater than or equal to, not equal to equal to ?42,4,40

H1:μis ?less than,less than or equal to,greater than,greater than or equal to,not equal to,equal to ?42,4,40

In the context of this test, what is a Type I error?

A Type I error is ?rejectingfailing to reject the hypothesis that μ is ?less than,less than or equal t,ogreater than, greater than or equal to,not equal to,equal to ?42,4,40 when, in fact,

μ is ?less than less than or equal to greater than greater than or equal to not equal to equal to ?42 4 40.

Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ?Type IType II

Answer 1

Given that we have to check whether the mean number of hours worked per week by college graduates, μ , is different from 40 hours

So, it is clear that it is a two tailed hypothesis test

We can hypotheses as

We know that type I error is the rejection of a true null hypothesis. So, type I error in this case would be the conclusion that the mean is different from 40 hourrs, when in fact, the mean is actually 40 hours

A Type I error is rejecting the hypothesis that μ is equal to 40 when, in fact,μ is equal to 40.

We know that whenever we reject the null hypothesis, then there is always chances of making a type I error only because we reject null hypothesis only in type I error, but not in type II error

So, answer is type I error