You are the manager of a restaurant for a  fast-food franchise. Last  month, the mean waiting time at the drive-through window for branches in your geographical  region, as measured from the time a customer places an order until the time the customer receives the  order, was 3.7 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.43  minutes, with a sample standard deviation of 0.9 minute. Complete parts  (a) and  (b) below.

 

a. At the 0.10 level of  significance, is there evidence that the population mean waiting time is different from 3.7 minutes? State the null and alternative hypotheses.

 

(Note: ? represents one of the following "≠, >, ≥, =, <, ≤"

____ represents an integer)

H₀ : μ ? ____

H₁ : μ ? ____

 

Determine the test statistic.

The test statistic is _____

 

Find the  p-value.

p-value = _____

 

State the conclusion.

Note: Choose one per ( )  

(Do not reject, Reject, Upper) H₀. There is (insufficient, sufficient) evidence to conclude that the population mean waiting time is different from 3.7 minutes.

 

b. Because the sample size is 81 , do you need to be concerned about the shape of the population distribution when conducting the t test in  (a)? Explain. Choose the correct answer below.

A. No, because n is equal to 81 , the sampling distribution of the t test is approximately normal. In  general, the t test is appropriate for a large sample size.

B. Yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. In  general, the t test is only appropriate for a normally distributed sample.

C.  No, because n is equal to 81, the sampling distribution of the t test is approximately normal. In  general, the t test is appropriate for this sample size unless the population is skewed.

D.  Yes, because n is equal to 81 , the sampling distribution of the t test cannot be determined. In  general, the t test requires a larger sample size.