A sample of employees at a large chemical plant was asked to indicate a preferen

Question

A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the 0.02 significance level Pension Plan Plan A Plan B Plan C 30 Job Class Supervisor Clerical Labor 35 35 40 34 42 48 ata Fil State the decision rule. Use 0.02 significance level. (Round your answer to 3 decimal places.) Ho: Pension plan preference and job class are not related H: Pension plan preference and job class are related Reject H0 if chi-square> Compute the value of chi-square. (Round your answer to 3 decimal places.) Chi-square

Explanation / Answer

Ans:

degree of freedom=(3-1)*(3-1)=4

significance level=0.02

critical chi square=chiinv(0.02,4)=11.668

Reject H0,if chi square is >11.668

Test statistic:

chi square=6.828

As,chi square=6.828<11.668,we fail to reject H0.

Observed(O) plan A plan B plan C Total Supervisor 35 30 34 99 Clerical 35 33 42 110 Labor 40 66 48 154 Total 110 129 124 363 Expected(E) plan A plan B plan C Total Supervisor 30.00 35.18 33.82 99 Clerical 33.33 39.09 37.58 110 Labor 46.67 54.73 52.61 154 Total 110 129 124 363 Chi square=(O-E)^2/E plan A plan B plan C Total Supervisor 0.833 0.763 0.001 1.598 Clerical 0.083 0.949 0.521 1.553 Labor 0.952 2.322 0.403 3.678 Total 1.869 4.034 0.925 6.828

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