Question

There are currently 45 U.S. Senators who are affiliated with the Democratic party and 53 who are affiliated with the Republican party. Using a Chi Square Goodness of Fit test with p > .05 significance, what conclusion can be made about the proportion of senators in each political party?

Group of answer choices

There is no significant difference in the proportion of Democratic and Republican U.S. Senators,χ2 (2) = 0.326, ns

There is no significant difference in the proportion of Democratic and Republican U.S. Senators,  χ2 (1) = 0.653, ns.

There are significantly more Republicans than Democrats in the U.S. Senate, χ2 (1) = 2.828, p < .05.

There are significantly more Republicans than Democrats in the U.S. Senate, χ2 (1) = 8, p < .05.

Answer 1

The expected value for each group = (45 + 53) / 2 = 98 / 2 = 49

Therefore the statistic is as below

	Observed	Expected	O-E	(O-E)2	(O-E)2/E
1	45	49	-4	16	0.327
2	53	49	4	16	0.327
Total	98	98			0.653

The p value for df = (2 - 1) = 1 is > 0.05, and hence we fail to reject the null, that there is a significant difference in the proportions.

Therefore Option 2: There is no significant difference in the proportion of Democratic and Republican US senators. (1) = 0.653, ns