Question

In the past, the mean lifetime of a certain type of radio battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a significance test to determine whether the mean lifetime has increased as a result. The hypotheses are:

H0: μ = 9.8 hours Ha: μ > 9.8 hours Explain the meaning of a Type I error.

A) Concluding that μ > 9.8 hours when in fact μ = 9.8 hours

B) Concluding that μ > 9.8 hours when in fact μ > 9.8 hours

C) Concluding that μ < 9.8 hours when in fact μ > 9.8 hours

D) Concluding that μ = 9.8 hours when in fact μ > 9.8 hours

E) Concluding that μ = 9.8 hours when in fact μ < 9.8 hours

Answer 1

Solution:

Given hypotheses are:

H0: μ = 9.8 hours Vs Ha: μ > 9.8 hours

We have to explain the meaning of a Type I error in the context of stated hypothesis.

Following are the definitions of Type I , Type II and correct decision.

Type I Error : Reject null hypothesis , in fact it is True.

Type II Error : Fail to reject null hypothesis , in fact it is False.

Correct decision: Reject H0, when it is False  or   Fail to reject H0, when it is True.

So according to definition of Type I Error : we reject null hypotheis H0: μ = 9.8 , in fact H0: μ = 9.8 is true.

So if we reject null hypothesis H0: μ = 9.8 then it means we conclude that mean μ > 9.8 hours, in fact μ = 9.8 is true.

Thus correct answer is:

A) Concluding that μ > 9.8 hours when in fact μ = 9.8 hours