1. Example 9.8 Analyzing Customer Waiting at R&P Supermarket Confidence Interval for the Difference Between Means

2. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Objective To use StatPro’s two-sample procedure to find a confidence interval for the difference between mean waiting times in the supermarket’s rush periods versus its normal periods.

3. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 SUPERMKT.XLS n As in Example 3.10, the manager of R&P Supermarket has collected a week’s worth of data on customer arrivals, departures and waiting. n This file contains the data from the 48 observations per day, each taken at the end of a half-hour period.

4. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Original Data

5. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Variables n The various times of the day are listed in the TimeInterval variable. They include Morning Rush, Morning, Lunch Rush, Afternoon, Afternoon Rush, Evening, and Night. n There is also a variable, EndWaiting, that records the number of customers still being served or waiting in line at the end of each half-hour period.

6. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Questions n The manager would like to check whether the average value of EndWaiting differs during rush periods from normal, non-night period. n She is concerned that there might be excessive waiting during rush periods, in which case she might need to add more checkout people during these times. n She plans to exclude the night because there normally is no waiting at that time of day.

7. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Solution n With the data set in the original form we need to perform three main steps: 1Rename the seven time intervals so that there are only three: Rush, Normal, and Night. 2“Unstack” the single EndWaiting variable so that there are three EndWaiting variables: one for Rush, one for Normal, and one for Night. 3Perform the statistical comparison between the EndWaiting variables for the Rush and Normal periods.

8. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Results n The results of Step 1 is in the New Data Sheet of SUPERMKT.XLS file. SUPERMKT.XLS n The results of Step 2 and 3 are in the Analysis sheet of the SUPERMKT.XLS file.SUPERMKT.XLS n The steps required to achieve these results are outlined in the next slides.

9. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Calculations 1 Copy sheet: Create a copy of the original data sheet by pressing Ctrl key and dragging the Original Data sheet tab to the right. Double click the new sheet and rename it NewData. 2 Rename time intervals: Use Excel’s Find and Replace feature to rename the time intervals on the NewData sheet. 3 Create boxplots: Use StatPro’s Boxplot procedure, using the unstacked variables on the Analysis sheet to create side-by-side boxplots of the EndWaiting variables.

10. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Supermarket Data with Time Categories Renamed

11. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Calculations -- continued 4 Perform Two-Sample Analysis: Use the Two- Sample Analysis menu item. Select the StatPro/Statistical Inference/Two-Sample Analysis menu item from the New Data sheet. Then select the Stacked option, select TimeInterval as the code variable, select Normal and Rush as the two categories to analyze, select EndWaiting as the measurement variable and ask for a 75% confidence interval.

12. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Boxplots

13. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Calculations -- continued n The boxplots show that –the distribution of EndWaiting is definitely skewed to the right for each time interval, with a number of outliers, and –the mean value of EndWaiting is slightly larger for Rush than for Normal, with Night a distant third. n The Two-Sample procedure shows that –the sample means of EndWaiting are 5.480 and 5.014 for the Rush and Normal periods –the sample standard deviations are 4.284 and 4.293 –these are based on sample sizes of 98 and 140 half hour periods

14. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Calculations -- continued n These summary statistics provide some evidence of different population variances. n A point estimate for the mean difference is -0.465 and that a 95% confidence interval for this mean difference extends from -1.578 to 0.648.

15. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Analysis of Supermarket Data

16. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Conclusions n What can the manager conclude from this analysis? Should she add extra checkout people during rush periods? n This is difficult to answer because it involves a trade- off between the cost of extra checkout people and the “cost” of making customers wait in line. n The manager does know from this analysis that the mean difference between rush and normal periods is rather minor.

17. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.7 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.79.99.109.119.129.139.149.15 Conclusions -- continued n Since the confidence interval extends from a negative value to a positive value, there is a good possibility that the true mean difference could be positive. n That is, the mean for normal times could be larger than the mean for rush times. n Therefore, the results of this analysis do not provide a strong incentive for the manager to change the current system.