Question

A psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown in the table below. Conduct a test of homogeneity. Test at a 5% level of significance.

	Open	Conscientious	Extrovert	Agreeable	Neurotic
Business	39	52	46	63	56
Social Science	73	77	63	81	67

a) What is the test statistic? (Round your answer to two decimal places.)

b) What is the p-value? (Round your answer to four decimal places.)

Answer 1

	Open	Conscientitious	Extrovert	Agreeable	Neurotic	Total
Business	39	52	46	63	56	256
Social Science	73	77	63	81	67	361
Column Total	112	129	109	144	123	617

Degrees of freedom = (r-1)(c-1) = (2-1)(5-1) = 4

The expected value of each group is calculated using the formula:

For each row r and column c,

where n_r = total number of corresponding row

n_c = total number of corresponding column

n =toal population size

For example,

Similarly,

E₂₁ = 65.53

E₁₂ = 53.52

E₂₂ = 75.48

E₁₃ = 45.23

E₂₃ = 63.77

E₁₄ = 59.75

E₂₄ = 84.25

E₁₅ = 51.03

E₂₅ = 71.97

The test statistic value is given by

b)

The p-value is 0.5125