You are conducting a multinomial Goodness of Fit hypothesis test for the claim t

Question

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table. Report all answers correct to three decimal places. Observed Expected Pearson Category Frequency Frequency Residual A18 ? 21 ? 25 D 21 What is the chi-square test-statistic for this data? For significance level alpha 0.05, what is the chi-square Critical Value? Critical Value- What would be the conclusion of this hypothesis test? Fail to reject the Null Hypothesis Reject the Null Hypothesis Report all answers accurate to three decimal places.

Explanation / Answer

applying chi square test of goodness of fit:

chi square test statistic =13.111

critical value for 0.05 level and (cateogories-1=4) degree of freedom =9.488

reject the null hypothesis

observed Expected Chi square category Oi Ei=total*p R2i=(Oi-Ei)2/Ei A 18.000 18.00 0.000 B 21.000 18.00 0.500 C 25.000 18.00 2.722 D 21.000 18.00 0.500 E 5.000 18.00 9.389 total 90 90 13.111

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