Using the critical value approach can the null hypothesis be

Using the critical value approach, can the null hypothesis be rejected for the following hypothesis test?

Test the following hypothesis for a multinomial probability distribution by using the Chi-Square goodness of fit test.

H0: Pa= 0.3, Pb = 0.5, Pc= 0.4

Ha: The probabilities are not Pa= 0.3, Pb = 0.5, Pc= 0.4

A sample of size 250 yeilded 120 in category A, 90 in category B, and 40 in category C. Use an alpha level of 0.05 and test to see whether the probabilities are as stated in H0.

Solution

Follwoing table shows the expected and observed frequencies for the abobe multinomial distribution:

You can see that sum of expected frequnency is not equal to observed frequency so chi-square test of goodness of fit cannot be apply. So null hypotheses rejected.