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Prior to a set of compensation policy changes at a company 31% of the employees surveyed...

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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 remainingemployees said that they were dissatisfied with their job. Now, ina survey of 194 employees, 76 said they liked their job very much,105 said that they liked their job moderately, and the remainingemployees said that they were dissatisfied with their job. Whentesting (at the 10% level of significance) whether the proportionshave changed, what is the critical value? (please round your answerto 3 decimal places)

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3.6 Ratings (609 Votes)

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
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