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	61	57
Social Science	71	75	62	81	65

a. What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

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

c. What is the p-value? (Round your answer to four decimal places.)
d. Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =  

Answer 1

The statistical software output for this problem is :

Contingency table results: Rows: var4 Columns: None Open Conscientious Extrovert Agreeable Neurotic Total Business 39 52 46 61 57 255 Social Science 71 75 62 81 65 354 Total 110 127 108 142 122 609 Chi-Square test: Statistic DF Value Chi-square 4 3.1766583 P-value 0.5287

Degrees of freedom = 4

Test statistics $\chi^2$ = 3.18

P-value = 0.5287

"do not reject" the null hypothesis

α = 0.05