Question

You may need to use the appropriate technology to answer this question. Test the following hypotheses by using the χ2 goodness of fit test. H0: pA = 0.40, pB = 0.40, and pC = 0.20 Ha: The population proportions are not pA = 0.40, pB = 0.40, and pC = 0.20. A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use α = 0.01 and test to see whether the proportions are as stated in H0.

(A) Use the p-value approach.

Find the value of the test statistic.

Answer 1

use expected value formula E[x]=n*p

Calculation for test statistic

Use excel function CHISQ.DIST.RT(x,df)

where x = 135.00 and degree of freedom = number of categories -1 = 3-1 =2

p-value = CHISQ.DIST.RT(135.00,2) = 0.0000

p-value(0.0000) < significance level (0.01), rejecting the null hypothesis

Sufficient evidence to reject the claim that the proportions are as stated in H0