The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associationʹs name. The associationʹs 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: $$\begin{array} { l }
\mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \
\mathrm { H } _ { \mathrm { A } } : \mathrm { p } 0.6
\end{array}$$ Define a Type II Error in the context of this problem.
A)They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.
B)They conclude that more than 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, in fact, that is not true.
D)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

Question

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associationʹs name. The associationʹs 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: $$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \
\mathrm { H } _ { \mathrm { A } } : \mathrm { p } > 0.6
\end{array}$$ Define a Type II Error in the context of this problem.
A)They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.
B)They conclude that more than 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, in fact, that is not true.
D)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

Quizplus · Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, it means failing to conclude that more than 60% of the association wants a name change when, in fact, more than 60% does want a change.

The State Association of Retired Teachers Has Recently Taken Flak H0:p=0.6HA:p>0.6\begin{array} { l } \mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \\\mathrm { H } _ { \mathrm { A } } : \mathrm { p } > 0.6\end{array}H0​:p=0.6HA​:p>0.6​

The State Association of Retired Teachers Has Recently Taken Flak $\begin{array} { l } \mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \\\mathrm { H } _ { \mathrm { A } } : \mathrm { p } > 0.6\end{array}$