Question

In 2010, 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 2010 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 2010 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes.

Answer 1

Answer: No, we do not have sufficient evidence to conclude that the mean call duration, µ, is different from the 2010 mean of 9.4 minutes.

Step-by-step explanation:

As per given , we have

$H_0: \mu=9.4\\\\H_a:\mu\neq9.4$, since $H_0$ is two-tailed so , the test is a two tail test.

Since population standard deviation is unknown, so we use t-test.

Critical value (two-tailed) for significance level of 0.01= $t_{n-1,\alpha/2}=t_{49, 0.005}\pm2.609228$

For n =50 , $\overline{x}=8.6$ and s= 4.8

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$t=\dfrac{8.6-9.4}{\dfrac{4.8}{\sqrt{50}}}\approx-1.18$

Since test statistic value (-1.18) lies in critical interval (-2.609228, 2.609228), it means the null hypothesis is failed to reject.

We do not have sufficient evidence to conclude that the mean call duration, µ, is different from the 2010 mean of 9.4 minutes.