A large electronics firm that hires many workers with disabilities wants to dete

Question

A large electronics firm that hires many workers with disabilities wants to determine whether their disabilities affect performance. Use the level of significance = 0.05 to decide on the basis of the sample data shown in the following table whether it is reasonable t maintain that the disabilities have no effect on the workers performance.

Above average

Average

Below average

blind

21

64

17

deaf

16

49

14

No disability

29

93

28

Above average

Average

Below average

blind

21

64

17

deaf

16

49

14

No disability

29

93

28

Explanation / Answer

The expected cell counts (based on the formula (row total *column total)/grand total are 20.34 63.48 18.18 15.75 49.17 14.08 29.91 93.35 26.74 To compute the chi square statistic we use the formula (observed-expected)^2/expected. So we have (21-20.34)^2 + (16-15.75)^2/15.75 +(29-29.91)^2/29.91 +( 64-63.48)^2+ (49-49.17)^2/49.17 + (93-93.35)^2/93.35 + (17-18.18)^2/18.18 + (14-14.08)^2/14.08+(28-26.74)^2/26.74 Total is 0.1954 Degrees of freedom are row count -1 times column count-1= 2*2=4 . Looking up in a chi square table with DF=4 the critical value at the .05 level is 9.49. Since our 0.1954< 9.49 we conclude that disabilities do not affect performance. (Remember in textbooks these days the politically correct answer is almost always the right one).

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