Question

Could you explain to how to find these answers in excel as well please? I am having a terrible time trying to get it to work correctly for me.

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 3.98 ​minutes, with a sample standard deviation of 0.9 minute. Complete parts​ (a) and​ (b) below.

​: mu=

: mu not equals

Determine the test statistic:

Find the P-value=                     (Rounded to the nearest three decimal places)

State the Conclusion:

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. 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 this sample size unless the population is skewed.

Answer 1

H0: mu = 3.7
Ha: mu not equals 3.7

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.98 - 3.7)/(0.9/sqrt(81))
t = 2.8

This is two tailed test, p-value = 2*P(t > 2.8)
= 0.006

Excel formula to calculate p-value =2 * (1 - T.DIST
(2.8,80,TRUE))

As p-value < 0.05, reject H0
There are significant evidence to conclude that the mean waiting time is different that 3.7

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 this sample size unless the population is skewed.