Illuminating Statistical Analysis Using Scenarios and Simulations

58For Part III

(A)   In the (Chi-squared) chapters, we wondered if the community could be considered 25% Democrat, 25% Republican, and 50% Independents: This forms the basis for the null hypothesis. We have gathered a random sample of 120 community members, so we'll be testing for counts of 30, 30, and 60. Table 58.1 shows assorted scenarios (A–K) of what we might find in terms of the number of D, R, and I in our sample of 120. Take a moment to study the table. For each scenario, note its sample count values, the Chi-squared sum that results, and the -value that is based on the magnitude of Chi-squared.

Table 58.1 Chi-squared test for goodness of fit.

D	R	I
Testing for	30	30	60
Sample count values				Chi-squared	-Value
Scenario A	40	40	40	13.33333	0.00127
Scenario B	38	38	44	8.53333	0.01403
Scenario C	36	36	48	4.80000	0.09072
Scenario D	34	34	52	2.13333	0.34415
Scenario E	32	32	56	0.53333	0.76593
Scenario F	30	30	60	0.00000	1.00000
Scenario G	28	28	64	0.53333	0.76593
Scenario H	26	26	68	2.13333	0.34415
Scenario I	24	24	72	4.80000	0.09072
Scenario J	22	22	76	8.53333	0.01403
Scenario K	20	20	80	13.33333	0.00127

(A1)   Which scenarios lead you to reject the ...