Question

QUESTION 11 2.326 points A political scientist is interested in the relationship between someone's political views and his or her optimism about the future. A random sample of American adults 18 and over was taken and the following questions were asked: 1). What are your political views (conservative, slightly conservative, moderate, slightly liberal, liberal)? This variable is called "POLITICS" for short). 2). When your children are the age you are at right now, what do you believe their standard of living will be (much worse, somewhat worse, about the same, somewhat better, much better)? This variable is called "OPTIMISM" for short) The researcher decides to conduct a chi-squared test of independence at the 0.05 level of significance. Using your answer to the previous question, what would be the decision in the context of the problem. Read carefully. Reject the null hypothesis and conclude that people with liberal views are less optimistic about their children's futures than people with conservative views. Fail to reject the null hypothesis. Conclude that people's political views directly influence their level of optimism about their children's futures. Reject the null hypothesis and conclude that people with conservative views are less optimistic about their children's futures than people with liberal views. Reject the null hypothesis and conclude that people's political views and their level of optimism about their children's futures are associated. Fail to reject the null hypothesis and conclude that there is not sufficient evidence to say whether people's political views are associated with their level of optimism about their children's futures.

Answer 1

H0: The out performed the market and Ranking are independent
H1: The out performed the market and Ranking are not independent

The observed frequencies are

	Yes	No	Total
Top	49	23	72
Middle	22	26	48
Bottom	38	25	63
Total	109	74	183

The expected frequencies are

	Yes	No	Total
Top	42.89	29.12	72
Middle	28.59	19.41	48
Bottom	37.53	25.48	63
Total	109	74	183

The chi square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
49	42.89	0.87
23	29.12	1.28
22	28.59	1.52
26	19.41	2.24
38	37.53	0.01
25	25.48	0.01
	Total:	5.93

Num Categories: 6
Degrees of freedom: 5

Test Statistic, X^2: 5.93
Critical X^2: 11.07051
P-Value: 0.3133

Here chisquare value < chisquare critical value and P-value > alpha 0.05 so we accept H0

Thus we conclude that the out performed the market and Ranking are independent