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:
$$\begin{array} { l }
\mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \
\mathrm { H } _ { \mathrm { A } } : \mathrm { p } 0.6
\end{array}$$
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, 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 more than $60 \%$ 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 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: 
$$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \
\mathrm { H } _ { \mathrm { A } } : \mathrm { p } > 0.6
\end{array}$$
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, 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 more than $60 \%$ 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 is rejected when it is actually true. In this context, it means concluding that more than 60% of the association wants a name change when, in fact, 60% or fewer want it.

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