Question

1)

1. 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.

   A. Select the null and alternative hypothesis of the test: ____ (enter option I or II)

   I)	H0: there is a relationship between gender and belief about human origins
   	Ha: there is no relationship between gender and belief about human origins
   II)	H0: there is no relationship between gender and belief about human origins
   	Ha: there is a relationship between gender and belief about human origins

   B. Results of the study are summarized in this table:

   		Belief about human origins
   		Religious texts	Evolutionary Theory	Total
   Gender	Male	30	36	66
   	Female	106	89	195
   	Total	136	125	261

   The degrees of freedom for the the Chi-square statistic are: ____ (enter a number: 1,2,3 or 4)

   The test statistic is X-squared =____, with a p-value = ____. (round answers to the nearest hundredth. Do not enter the 0 before the decimal point.)

   C. The conclusion of the test is: ____ (enter an option: a, b, c or d from the list below)

   1. Gender and belief about human origins are independent.
   2. Gender and belief about human origins are related.
   3. There is enough statistical evidence to suggest that gender and belief about human origins are related.
   4. There is not enough statistical evidence to suggest that gender and belief about human origins are related.

2)

1. What conditions need to be met to run a Chi-square test of independence?

   	a.	Variables must be related
   	b.	Variables must be independent
   	c.	Cell counts must be at least 5
   	d.	Expected cell counts must be at least 5

Answer 1

1A)

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

H_a: there is a relationship between gender and belief about human origin

b)

degree of freedom(df) =(rows-1)*(columns-1)=

1

applying chi square test:

Observed	Oi	religious	evolutionary	Total
	male	30	36	66
	female	106	89	195
	total	136	125	261
Expected	Ei=row total*column total/grand total	religious	evolutionary	Total
	male	34.39	31.61	66
	female	101.61	93.39	195
	total	136	125	261
chi square    χ2	=(Oi-Ei)2/Ei	religious	evolutionary	Total
	male	0.5606	0.6099	1.171
	female	0.1897	0.2064	0.396
	total	0.750	0.816	1.567

test statistic X² =1.57 and p value =0.21

c)

There is not enough statistical evidence to suggest that gender and belief about human origins are related.

2) Expected cell counts must be at least 5