In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes.
The hypotheses are: $$
\begin{array}{l}
\mathrm{H}_{0}: \mu=9.4 \text { minutes } \
\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4 \text { minutes }
\end{array}
$$
Explain the meaning of a correct decision.
A) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu=9.4 $ minutes OR concluding that $ \mu9.4 $ minutes when in fact $ \mu9.4 $ minutes
B) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu=9.4 $ minutes OR concluding that $ \mu \neq 9.4 $ minutes when in fact $ \mu \neq 9.4 $ minutes
C) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu \neq 9.4 $ minutes
D) Concluding that $ \mu \neq 9.4 $ minutes when in fact $ \mu=9.4 $ minutes

Question

In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes.
The hypotheses are: $$
\begin{array}{l}
\mathrm{H}_{0}: \mu=9.4 \text { minutes } \
\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4 \text { minutes }
\end{array}
$$
Explain the meaning of a correct decision.
A) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu=9.4 $ minutes OR concluding that $ \mu>9.4 $ minutes when in fact $ \mu>9.4 $ minutes
B) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu=9.4 $ minutes OR concluding that $ \mu \neq 9.4 $ minutes when in fact $ \mu \neq 9.4 $ minutes
C) Failing to reject the hypothesis that $ \mu=9.4 $ minutes when in fact $ \mu \neq 9.4 $ minutes
D) Concluding that $ \mu \neq 9.4 $ minutes when in fact $ \mu=9.4 $ minutes

Quizplus · Accepted Answer

A correct decision in hypothesis testing is either failing to reject the null hypothesis when it is true or rejecting the null hypothesis when the alternative hypothesis is true.

In 1990, the Average Duration of Long-Distance Telephone Calls Originating H0:μ=9.4 minutes Ha:μ≠9.4 minutes \begin{array}{l}\mathrm{H}_{0}: \mu=9.4 \text { minutes } \\\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4 \text { minutes }\end{array}H0​:μ=9.4 minutes Ha​:μ=9.4 minutes ​

In 1990, the Average Duration of Long-Distance Telephone Calls Originating $\begin{array}{l}\mathrm{H}_{0}: \mu=9.4 \text { minutes } \\\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4 \text { minutes }\end{array}$