Customers with "Premier Account" visiting the HSBC Baker Street Branch in London often complain that they have to wait for a long time before being served. To improve customer satisfaction, the branch manager carefully studied the customer arrival pattern and proposed a plan to rearrange bankers' lunch break to reduce customers' waiting time.

To evaluate if the plan is effective, the manager first asked an intern to randomly record the waiting time of 50 customers when bankers followed their original schedule (as summarized in the Before Improvement column in the data file Q3_bank.xlsx), and then asked the intern to again randomly record the waiting time of another 50 customers after the proposed plan was implemented.

Using the data in the column Before Improvement, construct a 95% confidence interval for the mean waiting time of customers before the change was made.

Data:

Before Improvement

13.1

12.42

11.96

9.56

2.46

16.4

9.8

11.24

13

8.42

12.62

10.9

10

8.7

0.4

5.5

14.9

9.8

8.8

14.6

17.2

4.3

1

13.9

10.6

1

9.9

14.1

11.5

3.2

14.9

18

8.2

16.1

14.3

13.5

1.5

12.7

5.4

14.9

9.5

11.4

5.7

4.2

10.8

10.5

14

4.4

13.4

18.6