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 the 4 categories occur with the following frequencies: H_0: p_A = 0.15, p_B = 0.4: p_C = 0.3: p_D = 0.15 Complete the table. Report all answers accurate to three decimal places. What is the chi-square test-statistic for this data? chi^2 = What is the P-Value? P-Value = For significance level alpha 0.1, What would be the conclusion of this hypothesis test? Reject the Null Hypothesis Fail to reject the Null Hypothesis

Explanation / Answer

From the given data we have

Degrees of freedom = 4 - 1 = 3

2 = [ (Oi - Ei)2 / Ei ] = 26.94

p-value = 0.00001

As p-value is less than significance level of 0.1, we reject the null hypothesis

Category pi Oi Ei=(pi*125) Oi - Ei (Oi - Ei)^2 (Oi - Ei)^2/Ei A 0.15 39 18.75 20.25 410.0625 21.87 B 0.4 35 50 -15 225 4.5 C 0.3 33 37.5 -4.5 20.25 0.54 D 0.15 18 18.75 -0.75 0.5625 0.03

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