Question

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.

Answer 1

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

Explanation:

Type 2 error results in a statistical analysis when a false null is incorrectly accepted.

The hypothesis Given :

H0: p = 0.6

HA: p > 0.6

The null in this context is that, the percentage of members who wants a name change is 60% ; while the alternative is that more than 60% wants a name change.

In this context, accepting a false null means Making a conclusion that exactly 60% wants a name change while it is actually FALSE.