In 1990, the average duration of long-distance telephone calls originating in one town was 8.5 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 8.5 minutes. A) $\mathrm { H } _ { 0 } : \mu \neq 8.5$ minutes $\mathrm { H } _ { \mathrm { a } } : \mu = 8.5$ minutes B) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes $\mathrm { H } _ { \mathrm { a } } : \mu 8.5$ minutes C) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes $\mathrm { H } _ { \mathrm { a } } : \mu \neq 8.5$ minutes D) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes $\mathrm { H } _ { \mathrm { a } } : \mu

Question

In 1990, the average duration of long-distance telephone calls originating in one town was 8.5 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 8.5 minutes.

A) $\mathrm { H } _ { 0 } : \mu \neq 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu = 8.5$ minutes

B) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes 
$\mathrm { H } _ { \mathrm { a } } : \mu > 8.5$ minutes

C) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu \neq 8.5$ minutes

D) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu < 8.5$ minutes

Quizplus · Accepted Answer

The null hypothesis ($H_0$) is typically a statement of no effect or no difference, so it should state that the current mean is equal to the historical mean (8.5 minutes). The alternative hypothesis ($H_a$) is what the test is trying to establish, in this case, that the mean has changed (either increased or decreased), hence $\mu \neq 8.5$ minutes.

In 1990, the Average Duration of Long-Distance Telephone Calls Originating H0:μ≠8.5\mathrm { H } _ { 0 } : \mu \neq 8.5H0​:μ=8.5

In 1990, the Average Duration of Long-Distance Telephone Calls Originating $\mathrm { H } _ { 0 } : \mu \neq 8.5$