1. A second example of Chi Square Imagine that the managers of a particular factory are interested in whether each line in their assembly process is equally accurate in making parts. The plant has four assembly lines.

2. What is the population in this situation? Since the question centers on product that comes off of the assembly line the population here is… –All parts from the four assembly lines.

3. Why is this a Chi Square problem? Since the data will represent the number of scrap parts in each line it is representing the number falling into each one of four categories – the categories being each production line.

4. What would be the frequency expected? The plant managers are asking whether each of the four production lines has equal number of errors in part production. –Since there are four production lines, if the errors occur equally across all lines each line should produce ¼ of all the errors. –This means that the should be 25% for each line.

5. What should be the frequency observed? This needs to represent the data that the plant managers collect from each line. –Assume that over a set period of time they record the number of scrapped parts that come from each of the four lines. –These data are: Line A Line B Line C Line D 108 140 133 119

6. What is the total n for this sampling? Line A Line B Line C Line D 108 140 133 119 n for the sample

7. The actual frequency expected Given this sample of 500 scrap parts…

8. Computing Chi Square Line A has 108 scrap parts:

9. Computing Chi Square cont. Line B has 140 scrap parts:

10. Computing Chi Square Line C has 133 scrap parts:

11. Computing Chi Square Line D has 119 scrap parts:

12. Computing Chi Square cont.

13. Evaluating Chi Square

14. Critical value df = k – 1 In this situation there were 4 groups (k=4) so df = 3

15. Probability of exceeding the critical value df 0.10 0.05 0.025 0.01 0.001 1 2.706 3.841 5.024 6.635 10.828 2 4.605 5.991 7.378 9.210 13.816 3 6.251 7.815 9.348 11.345 16.266 4 7.779 9.488 11.143 13.277 18.467 5 9.236 11.070 12.833 15.086 20.515 6 10.645 12.592 14.449 16.812 22.458 7 12.017 14.067 16.013 18.475 24.322 8 13.362 15.507 17.535 20.090 26.125 9 14.684 16.919 19.023 21.666 27.877 10 15.987 18.307 20.483 23.209 29.588 Critical value

16. Evaluating Chi Square Critical value: 7.815 Computed value: 4.912 Conclusion: There are no significant differences between the production lines in terms of # of scrap parts produced.