Question

In 2009, Gallup surveyed a random sample of American adults about their belief in the theory of evolution. The responses are summarized in the provided table.

Opinion Count:

Believe 397

Do Not Believe 254

No Opinion 367

a) a chi-square test appropriate for testing if all beliefs are not equally likely? Explain briefly. b) Test, at the 5% level, if there is evidence that not all opinions are equally likely. c) Which opinion contributes the most to the chi-square test statistic? For that opinion, is the observed count larger or smaller than we would expect?

Answer 1

Ans:

Expected count=1018/3=339.33

Opinion	Observed	Expected	(O-E)^2/E
Believe	397	339.33	9.80
Do not believe	254	339.33	21.46
No opinion	367	339.33	2.26
Total	1018	1018	33.51

a)Test statistic:

Chi square=33.51

b)df=3-1=2

p-value=CHIDIST(33.51,2)=0.000

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that all beliefs are not equally likely.

c)Do not believe contribute the most,as 21.46 is the largest contribution to chi square.

d)Observed count is smaller than expected for Do not believe opinion.