66 Six Sigma Case Studies with Minitab
®
FIGURE 5.7
Creation of contingency table for chi-square analysis.
Tabulated statistics: Importance of Candy Color, City
Using frequencies in Observed
Rows: Importance of Candy Color Columns: City
New York San
Boston Chicago Cleveland City Francisco All
1 92 29 38 53 62 274
2 63 58 46 36 70 273
3 98 100 82 41 125 446
4 480 478 326 263 486 2033
5 315 250 364 196 348 1473
6 257 203 405 304 252 1421
7 197 197 274 642 210 1520
All 1502 1315 1535 1535 1553 7440
Cell Contents: Count
FIGURE 5.8
Observed data.
67Chi-Square Analysis to Verify Quality of Candy Packets
FIGURE 5.9
Selection of “Expected cell counts” option.
Tabulated statistics: Importance of Candy Color, City
Using frequencies in Observed
Rows: Importance of Candy Color Columns: City
New York San
Boston Chicago Cleveland City Francisco All
1 92 29 38 53 62 274
55.3 48.4 56.5 56.5 57.2 274.0
2 63 58 46 36 70 273
55.1 48.3 56.3 56.3 57.0 273.0
3 98 100 82 41 125 446
90.0 78.8 92.0 92.0 93.1 446.0
4 480 478 326 263 486 2033
410.4 359.3 419.4 419.4 424.4 2033.0
5 315 250 364 196 348 1473
297.4 260.3 303.9 303.9 307.5 1473.0
6 257 203 405 304 252 1421
286.9 251.2 293.2 293.2 296.6 1421.0
7 197 197 274 642 210 1520
306.9 268.7 313.6 313.6 317.3 1520.0
All 1502 1315 1535 1535 1553 7440
1502.0 1315.0 1535.0 1535.0 1553.0 7440.0
Cell Contents: Count
Expected count
FIGURE 5.10
Observed data and expected data.
68 Six Sigma Case Studies with Minitab
®
For the P-value of the chi-square analysis, click on “Chi-Square” in the dia-
log box shown in Figure5.7, and the dialog box shown in Figure5.11 opens.
Check the box for “Chi-Square analysis” and click on “OK. It takes you back
to the dialog box shown in Figure5.7. Click on “OK” and the output shown in
Figure5.12 is the result. Because the Pearson chi-square P-value (0.000) is less
than 0.05, there are signicant differences among the ratings given by cus-
tomers in the various cities. In order to view the chi-square probability dis-
tribution plot, select “Probability Distribution Plot” as shown in Figure5.13.
Doing so opens the dialog box in Figure5.14. Select “View Probability” and
click on “OK. This opens the dialog box shown in Figure5.15. Select “Chi-
Square” from the drop-down menu for “Distribution” and enter “24” for
“Degrees of freedom” [The degrees of freedom are (number of ratings – 1)
* (number of cities – 1) = (7 – 1) * (5 – 1) = 6 * 4 = 24]. Click on “OK” and the
probability distribution plot shown in Figure5.16 is the result. Notice that
36.42 is the critical value of the chi-square characteristic. In order to add a
reference for the Pearson chi-square of 802.637 (refer to Figure5.12), right-
click on the plot shown in Figure5.16 and select “Reference Lines” as shown
in Figure5.17. Doing so opens the dialog box shown in Figure5.18. Enter
802.637” for “Show reference lines at X values” and click on “OK. The plot
shown in Figure5.19 is the result.
Now that it is clear that there are signicant differences among the ratings
given by customers in the various cities and that New York City seems to give
a lot more importance to candy color than the other cities (see Figure5.5), the
company wants to check whether its claim of the following percentages in a
packet are correct: 14% yellow candy, 13% red candy, 20% orange candy, 24%
blue candy, 16% green candy, and 13% purple candy. To this end, a packet
of candy is randomly selected, and the number of candies of each color is
counted. The collected data are in the CHAPTER_5_2.MTW worksheet (the
FIGURE 5.11
Selection of “Chi-Square analysis” option.

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