Question

Prior to a set of compensation policy changes at a company 31% 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 194 employees, 76 said they liked their job very much, 105 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)

Answer 1

Ho: proportions have not changed

H1: proportions have changed

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency  
total frequency=   194

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
very much	76	0.3100	60.14			4.183
moderately	105	0.5000	97			0.660
dissatisfied	13	0.1900	36.86			15.445

chi square test statistic,X² = Σ(O-E)²/E =   20.287              
                  
level of significance, α=   0.1              
Degree of freedom=k-1=   3   -   1   =   2

Critical value =    4.605 [ Excel function: =chisq.inv.rt(α,df) ]      

since, test stat > critical value, reject Ho