Question

A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.24 minutes. The population standard deviation is assumed to be 0.40 minutes. Can the claim be supported at α=0.08?
a. Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported.
b. No, since test statistic is not in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported.
c. No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported.
d. Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported.

Answer 1

Answer:

(A) Yes, since the test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported.

Step-by-step explanation:

Null hypothesis: The wait time before a call is answered by a service representative is 3.3 minutes.

Alternate hypothesis: The wait time before a call is answered by a service representative is less than 3.3 minutes.

Test statistic (t) = (sample mean - population mean) ÷ sd/√n

sample mean = 3.24 minutes

population mean = 3.3 minutes

sd = 0.4 minutes

n = 62

degree of freedom = n - 1 = 62 - 1 = 71

significance level = 0.08

t = (3.24 - 3.3) ÷ 0.4/√62 = -0.06 ÷ 005 = -1.2

The test is a one-tailed test. The critical value corresponding to 61 degrees of freedom and 0.08 significance level is 1.654

Conclusion:

Reject the null hypothesis because the test statistic -1.2 is in the rejection region of the critical value 1.654. The claim is contained in the alternative hypothesis, so it is supported.