A second example of Chi Square

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 (k4) 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
• 7.779 9.488 11.143 13.277
  18.467
• 9.236 11.070 12.833 15.086
  20.515
• 10.645 12.592 14.449 16.812
  22.458
• 12.017 14.067 16.013 18.475
  24.322
• 13.362 15.507 17.535 20.090
  26.125
• 14.684 16.919 19.023 21.666
  27.877
• 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.