Which of the following statements describes a Type II error in hypothesis testin

Question

Which of the following statements describes a Type II error in hypothesis testing?

A. A court declares a defendant guilty, when he is actually innocent.          

B. A scientist, trying to support a theory about the number of different species of animals in a particular country, declares the null hypothesis to be "there are 715 different species" when there are actually more than 800.    

C. A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4.            

D. Through hypothesis testing, we find the alternative hypothesis to be true when it is actually false.

Explanation / Answer

A type II error is incorrectly failing to reject a false null hypothesis.

Hence,

OPTION C: C. A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4.

[In this case, Ho: u = 1.4, H1: u > 1.4, so he failed to reject Ho when it is false.]

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