Prior to a set of compensation policy changes at a company 28% of the employees

Question

Prior to a set of compensation policy changes at a company 28% of the employees surveyed said that they liked their job very much, 50% said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. Now, in a survey of 206 employees, 77 said they liked their job very much, 104 said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. When testing (at the 5% level of significance) whether the proportions have changed, what is the critical value? (please round your answer to 3 decimal places)

Explanation / Answer

for applying chi square test :

for 0.05 level and 2 degree of freedom ; critical value=5.991

as test stat is higher then critical value we reject null hypothesis abd conclude that  the proportions have changed

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E like very much 0.28 77.00 57.68 6.47 like moderately 0.50 104.00 103.00 0.01 dissatisfied 0.22 25.00 45.32 9.11 206 206 15.592

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