You are the manager of a restaurant for a fast-food franchise. Last month, the m

Question

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 3.9 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.77 minutes, with a sample standard deviation of 0.9 minute.

a. At the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes?
- State the null and alternative hypotheses.
- Determine the test statistic.
- Find the p-value.
- State the conclusion.

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. 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.
B. 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.
C. 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.
D. 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.

Explanation / Answer

a) standard deviation = 0.9

U=3.9

Rejection region T Stat < -1.9983 or T Stat > 1.9983

(3.77 – 3.9) / ( (0.9 )/ (SQRT81) = -0.13 / 0.1 = -1.3

The critical value for the 0.05 significance level is -1.645. So there is not sufficient evidence to support the claim that the new process results in a shorter waiting time.

b) The sample size of 81 is large enough to ensure that the sampling distributionis normal. You don’t have to be concerned about the shape of the populationdistribution when conducting the T Test in (A). In general, the T test isappropriate for the sample size except for cases where the population isextremely left skewed or right skewed

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