Question

1. Use the data in the contingency table to answer the question.

	Columns
Rows	1	2	3	Total
1	36	35	92	163
2	67	57	113	237
Total	103	92	205	400

You wish to test the null hypothesis of "independence"—that the probability that a response falls in any one row is independent of the column it falls in—and you plan to use a chi-square test. You are given that there are 2 degrees of freedom associated with the test statistic Χ². You are also given the value of the test statistic Χ² = 3.16.

Find the rejection region for α = 0.05. (Round your answer to two decimal places.)

Χ² > ____________

2. Conduct the appropriate test of the specified probabilities using the given information. Use α = 0.05.

The five categories are equally likely to occur, and the category counts are shown in the table

Category	1		2		3		4		5
Observed Count	46		65		73		53		63

Find the test statistic. (Round your answer to two decimal places.)

Χ^{2=______________}

Answer 1

1)

for 2 df and 0.05 level of signifcance critical region       χ2=

5.991

rejection region x² >5.99

2)

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.200	46.000	60.00	-1.81	3.267
2	0.200	65.000	60.00	0.65	0.417
3	0.200	73.000	60.00	1.68	2.817
4	0.200	53.000	60.00	-0.90	0.817
5	0.200	63.000	60.00	0.39	0.150
total	1.000	300	300		7.4667
test statistic X2 =		7.47