A bank branch located in a commercial district of a city has

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon- to- 1:00 P. M. lunch period. The waiting time (defined as the time the customer enters the line until he or she reaches the teller window) of all customers during this hour is recorded over a period of a week. To see if the population mean waiting time is now less than 5 minutes, a random sample of 15 customers is selected, and the results are as follows:

4.50   6.10   0.38   5.12   6.46   6.19   3.79   4.21  

5.55   3.02   5.13   4.77   2.34   3.54   3.20

a. State the null and alternative hypothesis.

b. Compute the sample mean, standard deviation, Test Statistic, and p-value.

c. At ? = 0.05 level of significance, is there evidence that the population mean waiting time is less than 5 minutes? Write your answer in a sentence and report the p-value.

Solution

a. State the null and alternative hypothesis.

Let mu be the population mean

Null hypothesis: mu=5

Alternative hypothesis: mu <5

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b. Compute the sample mean, standard deviation, Test Statistic, and p-value.

sample mean=4.286667

standard deviation=1.637985

the test statisitc is

t=(xbar-mu)/(s/vn)

= (4.286667 -5)/(1.637985/sqrt(15))

=-1.69

The degree of freedom =n-1=15-1=14

It is a left-tailed test.

So the p-value= P(t with df=14 <-1.69) =0.0566 (from student t table)

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c. At ? = 0.05 level of significance, is there evidence that the population mean waiting time is less than 5 minutes? Write your answer in a sentence and report the p-value.

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that there is evidence that the population mean waiting time is less than 5 minutes