Test the following hypotheses by using the 2 goodness of fit test. H0: pA = 0.4,

Question

Test the following hypotheses by using the 2 goodness of fit test. H0: pA = 0.4, pB = 0.2, and pC = 0.4 Ha: The population proportions are not pA = 0.4, pB = 0.2, and pC = 0.4 A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use = .01 and test to see whether the proportions are as stated in H0. Use Table 12.4.

a. Use the p-value approach. 2 = (to 2 decimals)

b. The p-value is

c. Repeat the test using the critical value approach. 2.01 = (to 3 decimals)

Conclusion:

Explanation / Answer

Ans:

Expected count can be calculated as: 200*0.4=80,200*0.2=40,200*0.4=80 for A,B and C respectively.

Test statictic:

chi square score=200

df=3-1=2

p-value=CHIDIST(200,2)=0

As,p-value<0.01,we reject null hypothesis.

critical chi square value=CHIINV(0.01,2)=9.21

(as chi square test statistic=200>9.21,we reject null hypothesis.)

There is not sufficient evidence to conclude that the proportions are as stated in H0

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