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.