Determine whether the outcome is a Type I error, a Type II error, or a correct decision.

Question

A test is made of Hv0 : u = 30 versus Hv1 : u does not = 30.
The true value of u is 30, and Hv0 is rejected.

The outcome of this test is a [blank]

Answer 1

The outcome of this test is a Type I error.

A Type I error occurs when the null hypothesis (H0) is rejected when it is actually true. In this case, the null hypothesis (H0: µ = 30) is true since the true value of µ is indeed 30, but it was rejected. Hence, a Type I error is made.

Answer 2

A computer magazine editor claims that the mean cost of a gaming computer is $1250. A test is made of Hv0 : u=1250 versus Hv1 : u does not equal 1250. The null hypothesis is not rejected. State an appropriate conclusion.

There [is or isnt] enough evidence to conclude that the mean cost is [more than? less than? different than?] $1250

Answer 3

There isn't enough evidence to conclude that the mean cost is different than $1250.

Since the null hypothesis (H0: µ = 1250) is not rejected, we do not have sufficient evidence to state that the mean cost of a gaming computer differs from $1250.