Question

Is the religious make-up of the United States Congress reflective of that in the general population? The following table shows the religious affiliation of the 535 members of the 114th Congress (2015-2017) along with the religious affiliation of a random sample of 1200 adult Americans. Perform a complete hypothesis test to answer the question. Explain everything!

protestant	306	616
Catholic	164	287
Mormon	16	20
Orthodox Christian	5	7
Jewish	28	20
Buddhist/Muslim/Hindu/Other	6	57
Unaffiliated/dont know/Refused	10	193

Answer 1

Here, we are trying to test whether religious make-up of the United States Congress is reflective of that in the general population, therefore this is a case of chi square test for goodness of fit here.

The observed frequencies here are the set of frequencies given for the US congress.

The expected proportions for the country here are computed as:

= Frequency for country / Total frequency

Religion	O_i	Country O_i	p_i	E_i	(O_i -E_i)^2/E_i
protestant	306	616	0.5133	274.6333	3.5825
Catholic	164	287	0.2392	127.9542	10.1544
Mormon	16	20	0.0167	8.9167	5.6269
Orthodox Christian	5	7	0.0058	3.1208	1.1315
Jewish	28	20	0.0167	8.9167	40.8419
Buddhist/Muslim/Hindu/Other	6	57	0.0475	25.4125	14.8291
Unaffiliated/dont know/Refused	10	193	0.1608	86.0458	67.2080
	535	1200		535	143.3744

The expected frequency for the Congress members religious make up here are computed here as:
E_i = p_i * 535 which is the total frequency here. These are computed in the above table.

The chi square test statistic now is computed here as:

For n - 1 = 6 degrees of freedom, we get from the chi square distribution tables, the p-value here as:

As the p-value here is approx. 0, therefore the test is significant here and we have sufficient evidence here that the religious make-up of the United States Congress is not reflective of that in the general population,