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 3.9minutes

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.**

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