Question

In: Statistics and Probability

Solve the problem. The State Association of Retired Teachers has recently taken flak from some of...

Solve the problem.

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses:

H0: p = 0.6
HA: p > 0.6

Define a Type II Error in the context of this problem.

  

A.They conclude that more than 60% of the association wants a name change when, in fact, that is not true.

B.They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

C.They conclude that more than 60% of the association wants a name change when that is, in fact, true.

D.They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

why is A wrong? which is correct?

Solutions

Expert Solution

Solution :

The null and alternative hypotheses are as follows :

H​​​​​​0 : p = 0.6 i.e. Exactly 60% of the association wants a name change.

H​​​​​​A : p > 0.6 i.e. More than 60% of the association wants a name change.

Type II error is defined as follows :

The error committed by not rejecting the null hypothesis, when actually the null hypothesis is false is known as type II error.

Now for the given hypothesis, if they are not rejecting the null hypothesis then it means that they are concluding that exactly 60% of the association want a names change. Hence, for the given hypothesis the type II error would be as follows :

They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

Hence, option (D) is correct.

In option A, they are concluding that more than 60% of the association wants a name change, it means they are rejecting the null hypothesis, which doesn't match to the definition of type II error. Therefore option (A) is not correct.

Please rate the answer. Thank you.

orchestra answered 1 year ago
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