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 I Error in the context of this problem.
A)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.
B)They conclude that more than 60% of the association wants a name change when, in fact, that is not 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.

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 I Error in the context of this problem.
A)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.
B)They conclude that more than 60% of the association wants a name change when, in fact, that is not 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.

Quizplus · Accepted Answer

A Type I Error occurs when the null hypothesis ($H_0$) is rejected when it is actually true. In this context, rejecting $H_0$ means concluding that more than 60% of the association wants a name change when, in reality, this is not true.

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 $\begin{array} { l } \mathrm { H } _ { 0 : \mathrm { p } } = 0.6 \\\mathrm { H } _ { \mathrm { A } } : \mathrm { p } > 0.6\end{array}$