Question

The data table contains waiting times of customers at a​ bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than

2.4

​minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of

0.01.

Complete parts​ (a) through​ (d) below.

Customer Waiting Times

​(in minutes)

7.5

6.5

9.2

6.2

6.2

6.8

7.9

7.7

7.2

6.2

6.4

7.6

7.3

6.4

12.5

6.8

6.8

6.6

13.3

6.6

6.1

6.3

6.6

4.1

6.1

7.4

7.2

6.4

6.7

7.5

7.1

7.8

8.7

7.9

6.5

8.7

6.5

6.5

8.2

7.6

7.6

6.9

10.8

7.9

8.9

6.6

8.3

6.1

9.2

6.6

6.2

6.8

7.5

7.6

6.8

8.9

6.9

7.7

7.5

6.4

Answer 1

(1) Nail and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:0 2.4 Ha: 0 < 24 This corresponds to a left-tailed test, for which a Chi-Square test for one population variance will be used. (2) Rejection Region Based on the information provided the significance level is a = 0.01, and the the rejection region for this left-tailed test is R = {x* : x* < 36.698} (3) Test Statistics The Chi-Squared statistic is computed as follows: (n-1)s (60 - 1)-2.1321 21.839 5.76 (4) Decision about the nul hypothesis Since it is observed that x = 21.839<xi = 36.698, it is then concluded that the null hypothesis is rejected

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the standard deviation of waiting times is less than  2.4   at the 0.01 significance level.