Question

Externalizers and Internalizers are two categories of personality types in a personality theory by Rotter. A large group of people at a PTA meeting were given a brief personality test and then classified as lower, middle, or upper class. Test to see if there is a relationship between SES and Externalizers and Internalizers. Write out your results and conclusions. Must show all work including the expected frequencies, chi square calculations, as well as LaTeX: \phi ? df and critical value for credit.

	Lower	Middle	Upper
Internalizers	8	36	12
Externalizers	18	21	2

Answer 1

Null Hypothesis H0: The personality types(Externalizers and Internalizers ) are independent of classes(lower, middle, or upper).

Alternative Hypothesis H1: The personality types(Externalizers and Internalizers )  are depends on classes(lower, middle, or upper).

Under H0, the expected frequencies are

	(Obs. Freq.)				(Exp. Freq.)
	Lower	Middle	Upper	Total	Lower	Middle	Upper	Total
Internalizers	8	36	12	56	15.01	32.91	8.08	56.00
Externalizers	18	21	2	41	10.99	24.09	5.92	41.00
Total	26	57	14	97	26	57	14	97.00
	Calculations For Chi Square
	Obs freq( O )	Exp. Freq. ( E )	(O-E)^2/E
	8	15.01	3.274
	36	32.91	0.290
	12	8.08	1.902
	18	10.99	4.471
	21	24.09	0.396
	2	5.92	2.596
Total	97	97	12.929

Under H0, the test statistic is

Degrees of freedom = (r-1)*(c-1) = (2-1)*(3-1)= 2

The critical value of Chi square for 2 df at 5% significance level is 5.991

The P-Value is 0.0016

Since p value is less than significance level, REject H0.

Hence , the personality types(Externalizers and Internalizers )  are depends on classes(lower, middle, or upper).