Question

In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes. H0: μ < 7.2 minutes Ha: μ > 7.2 minutes H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes H0: μ = 7.2 minutes Ha: μ ≤ 7.2 minutes H0: μ ≠ 7.2 minutes Ha: μ = 7.2 minutes

Answer 1

We know that In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. And we want to test if the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes (alternative hypothesis) and the complement rule would represent the null hypothesis.

The correct system of hypothesis are:

Null hypothesis:
`\mu =7.2`

Alternative hypothesis:
`\mu \\eq 7.2`

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

Explanation:

We know that In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. And we want to test if the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes (alternative hypothesis) and the complement rule would represent the null hypothesis.

The correct system of hypothesis are:

Null hypothesis:
`\mu =7.2`

Alternative hypothesis:
`\mu \\eq 7.2`

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

And in order to test the hypothesis we can use a one sample t test or z test depending if we know the population deviation or not