Problem Set 1: Chi Square Test of Goodness of Fit Research Scenario: A political psychologist is curious about the effects

A political psychologist is curious about the effects of a town hall meeting on people’s intentions to support a state proposition that would legalize gambling. He interviews people as they leave and asks them whether their opinion about the proposition has changed as a result of the meeting. He records these frequencies in the table below.

Here we have given three categories less likely to support, no change and more likely to support.

Hypothesis for the test is,

H : p1 = p2 = p3  

H1 : Atleast one population proportion differ.

Assume alpha = level of significance = 0.05

We have given observed frequencies. Now we need to find expected frequencies.

The formula for expected frequencies is,

E = N * p

where p is probability.

Assume three categories are equally likely.

So probability for each category will be 1/3

N = sample size = 46

E1 = E2 = E3 = (1/3)*46 = 15.33

The test statistic is,

Test statistic = 9.43

Now we have to find P-value for taking decision.

P-value we can find in excel.

syntax :

=CHIDIST(x, deg_freedom)

where x is test statistic.

deg_freedom = k-1 = 3-1 = 2

P-value = 0.0089

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one population proportion differs.

Bar chart :