Prior to a set of compensation policy changes at a company 29% of the employees

Question

Prior to a set of compensation policy changes at a company 29% of the employees surveyed said that they liked their job very much, 52% said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. Now, in a survey of 208 employees, 75 said they liked their job very much, 110 said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. When testing (at the 10% level of significance) whether the proportions have changed, what is the critical value? (please round your answer to 3 decimal places)

Explanation / Answer

by applying chi square test :

here for 2 degree of freedom critical vlaue at 0.1 level of significance =4.605

as test stat X2=10.51 is higher then critical value we reject nullhypothesis and conclude that proportions have changed

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E like very much 0.29 75.00 60.32 3.57 like moderately 0.52 110.00 108.16 0.03 dissatisfied 0.19 23.00 39.52 6.91 208 208 10.5096

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