Goodness of fit test. Suppose we have a multinomial population with four categories: A, B, C, and D. The null hypothesis is that the proportion of items is the same in every category. The null hypothesis is

H₀: pA = pB = pC = pD = 0.25

A sample of size 300 yielded the following results. A:85, B:95, C:50, D:70

Qs. 1: What is the value of the test statistic?

Hint:

Step 1. You are given observed and expected frequencies. Find the difference of Observed -Expected. Be sure to compute the expected frequencies by multiplying the proportions by sample size first.

Step 2: Square the difference and divide by the respective expected frequencies.

Step 3: Sum the values obtained in step 2. This is the test statistic.

Qs. 2. Use =.05 to determine whether the null hypothesis should be rejected. What are your conclusions?

Hint:

Step 1: In Excel, Use the CHISQ.TEST(range of observed values, range of expected values) to get the p-value.

Step 2: Reject null of no change if p<0.05