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 3.8 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.55 ?minutes, with a sample standard deviation of 0.9 minute. Complete parts? (a) and? (b) below. a. At the 0.05 level of? significance, is there evidence that the population mean waiting time is different from 3.8 ?minutes? State the null and alternative hypotheses. Upper H 0?: mu ? greater than greater than or equals not equals equals less than less than or equals nothing Upper H 1?: mu ? greater than or equals less than not equals equals less than or equals greater than nothing ?(Type integers or? decimals.) Determine the test statistic. The test statistic is nothing. ?(Round to two decimal places as? needed.) Find the? p-value. ?p-valueequals nothing ?(Round to three decimal places as? needed.) State the conclusion. ? Do not reject Reject Upper H 0. There is ? insufficient sufficient evidence to conclude that the population mean waiting time is different from 3.8 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.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 3.8
H_A : ? ? 3.8

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	3.55	0.1	80	-2.5	0.0145

Hence,

Hypotheses:

H₀ : ? = 3.8
H_A : ? ? 3.8

Test statistic = -2.5

p - Value = 0.015

Reject; Sufficient

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. Option C is correct.