Question

Suppose youare interested in whether the distribution of religious affiliations of members of the House of Representatives is the same as the distribution of religious affiliation in the United States. The following table contains data for religiousaffiliation:

Religion	Proportion in US1	Number of Representatives2
Protestant	46.5%	220
Catholic	20.8%	140
Other Christian	3.3%	36
Jewish	1.9%	19
Other/None	27.4%	20
TOTAL	100.0%	435
1 data from http://www.pewforum.org/2015/05/12/americas-changing-religious-landscape/ 2 data from https://www.washingtonpost.com/graphics/politics/114th-house-religions/

1. What type of hypothesis test would you use for this?
a. Goodness of Fit
b. Test of Heterogeneity
c. Test of Independence

2. What is the p-value for the test?

3. Is the distribution of religious affiliations for Congressmen and Congresswomen different than the distribution in the US?

Answer 1

1)a. Goodness of Fit

2)

applying chi square goodness of fit:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Protestant	0.465	220.000	202.28		1.553
Catholic	0.208	140.000	90.48		27.102
Other Christian	0.033	36.000	14.36		32.637
Jewish	0.019	19.000	8.27		13.94
Other/None	0.274	20.000	119.19		82.55
total		435	435		157.78

for above test staitistic 157.78 and (groups-1=5-1=4) degree of freedom p value =0.0000

3)

as p value is highly significant we reject null hypothesis

we have highly sufficient evidence to conclude that  distribution of religious affiliations for Congressmen and Congresswomen different than the distribution in the US