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 64 orders. The sample mean waiting time is 3.67 ​minutes, with a sample standard deviation of 0.8 minute. Complete parts​ (a) and​ (b) below.

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.

H 0​: u =  ____

H 1​: u not = ____ ​(Type integers or​ decimals.)

Determine the test statistic.

The test statistic is ____.

​(Round to two decimal places as​ needed.)

Find the​ p-value. ​

p-value = ____ ​(Round to three decimal places as​ needed.)

State the conclusion. ▼ Do not reject/Reject , H 0. There is ▼ sufficient/ insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes.

b. Because the sample size is 64​, 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 64​, 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.

B. ​Yes, because n is equal to 64​, the sampling distribution of the t test cannot be determined. In​ general, the t test requires a larger sample size.

C. ​Yes, because n is equal to 64​, the sampling distribution of the t test cannot be determined. In​ general, the t test is only appropriate for a normally distributed sample.

D. ​No, because n is equal to 64​, the sampling distribution of the t test is approximately normal. In​ general, the t test is appropriate for a large sample size.

Answer 1

Given

different from 3.9​minutes

So two tailed t test

Determine the test statistic.

t=xbar-mu/s/sqrt(n)

t=(3.67-3.9)/(0.8/sqrt(64))

t=-2.30

Find the​ p-value. ​

df=n-1=64-63

p value is

=T.DIST.2T(2.3;63)

=0.024772485

p=0.025

p<0.05

Reject Ho.

There is ▼ sufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes.

Solutionb:

n=64

large sample as n>30

sample follows normal distribution

A. ​No, because n is equal to 64​, 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.