Question

1n 2015, the average duration of long-distance telephone calls from a certain town was 9.4 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Twenty calls, originating from the town, was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes

a) Using a 1% level of significance, Complete the following:

i. Give the null and alternative hypothesis of this test.

ii. Determine the critical value(s) of this test.

iii. Compute the value of the test statistic.

iv. State the decision rule.

v. Give your decision based on the available sample evidence.

vi. Hence, state your conclusion

Answer 1

i)

$H_0:\mu=9.4$ min, the average duration of long-distance telephone calls is 9.4min

$H_a:\mu\neq9.4$ min, the average duration of long-distance telephone calls is not 9.4min

ii)

critical value:

for $df=n-1=20-1=19$

$t_{crit}=2.861$

iii)

test statistic:

$t=\frac{\overline{x}-\mu}{\sigma/n}=\frac{10.2-9.4}{4.8/\sqrt{20}}=0.745$

iv)

if $|t|<t_{crit}$ then we accept the null hypothesis;

if $|t|\ge t_{crit}$ then we reject the null hypothesis

v)

Since $|t|<t_{crit}$ we accept the null hypothesis.

vi)

The average duration of long-distance calls has not changed.