Suppose youare interested in whether the distribution of religious affiliations
ID: 3368979 • Letter: S
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?
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/
Explanation / Answer
1)a. Goodness of Fit
2)
applying chi square goodness of fit:
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
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 435 435 157.78Related Questions
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