Question

A research study wanted to examine whether religious belief and gender are related in their state. They selected a representative sample of men and women in their State.

Select the null and alternative hypothesis of the test: H0: there is a relationship between gender and belief about human origins Ha: there is no relationship between gender and belief about human origins H0: there is no relationship between gender and belief about human origins Ha: there is a relationship between gender and belief about human origins

Results of the study are summarized in this table for the Belief about human origins: religious texts evolutionary theory total male 30 36 66 female 102 89 191 total 132 125 259

The degrees of freedom for the the χ2 statistic are Round the following numbers to two places after the decimal: The test statistic is χ2 =

with a p-value =

The conclusion of the test at the 5% significance level is Gender and belief about human origins are related. There is not enough statistical evidence to suggest that gender and belief about human origins are related. Gender and belief about human origins are independent. There is enough statistical evidence to suggest that gender and belief about human origins are related.

Answer 1

Correct answer:

H0: there is no relationship between gender and belief about human origins

Ha: there is a relationship between gender and belief about human origins

The observed frequencies are

	male	female	Total
religious texts	30	36	66
evolutionary theory	102	89	191
Total	132	125	257

The expected frequencies are

	male	female	Total
religious texts	33.899	32.101	66
evolutionary theory	98.101	92.899	191
Total	132	125	257

The chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
30	33.899	0.4485
36	32.101	0.4736
102	98.101	0.155
89	92.899	0.1636
	Total:	1.2407

Degrees of freedom: 1

Test Statistic, X^2: 1.2405
Critical X^2: 3.841456
P-Value: 0.2654

since chi-square value < chi-square critical value so we do not reject H0

and P-value > alpha 0.05 so we accept H0

Thus we conclude that there is no relationship between gender and belief about human origins

i.e.  Gender and belief about human origins are independent.