Question

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1:00pm lunch period. The waiting time of all customers during this hour is recorded over the period of a week. A random sample of 30 customers is selected and their waiting time is recorded (see data file Bank 1). At the 0.05 level of significance is there evidence that the population mean waiting time is less than 5 minutes?

4.21

5.55

3.02

5.13

4.77

2.34

3.54

3.20

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

4.50

6.10

0.38

5.12

6.46

6.19

3.79

Usethe full 5 step hypothesis testing procedure as demonstrated in class.

Identify information given in the question.

1. Select appropriate test statistic

2. State Hypotheses:   (Null and Alternative)

3.   Determine critical value(s) and state decision rules.

4.   Collect data and compute test statistic

5.     a. Make a Decision :

- either reject the null

- or fail to reject (FTR) the null.

b. State the managerial conclusion

Answer 1

Step 1: Stating the null and alternative hypothesis

Let denote the population mean waiting time.

To test:    Vs  

Step 2: Test statistic and Significance level

Test statistic appropriate here, is given by

(We chose t test for testing the mean since, the population variance is unknown)

From the given data,

  

  

Given that n = 30 and significance level is fixed at 0.05.

Step 3. Decision rule

Since our test is left tailed, the decision rule, here, is to reject H₀ when

From t tables,

Hence, the rejection region is

Step 4. Compute the test statistic:

From the given data,

  

  

And given that n = 30, substituting the values obtained in the test statistic formula:

                

Since, t = -2.428 < -1.699, the test statistic falls in the rejection region.

Step 5. Interpretation

Since, the test statistic falls in the rejection region, we may reject H₀ at 5% level of significance. It implies that we have sufficient evidence to support our claim that the population mean waiting time is less than 5 minutes based on the given data.

Hence we may conclude that population mean waiting time of the customers is less than 5 minutes.