Question

#1. A survey organization recently conducted a random sample of 1000 individuals from the population of American adults. The survey assessed the relationship between religiosity and partisanship. It asked the individuals whether religion is an important part of your life,” and asked them if they think of themselves as Democrats, Republicans, or Independents. The results were as follows:

Partisanship	Religion Not Important	Religion Important	Total
Democrat	130	220	350
Independent	85	255	340
Republican	35	275	310
Total	250	750	1000

a. Construct a 99.7% confidence interval for the proportion of American adults who claim that religion is important to them. Show your work and tell us what your results suggest about the overall population of all American adults.

b. Use a difference in proportions test to assess whether one can be 95% confident that the proportion of religious Americans who are Democrats differs from the proportion of religious Americans who are Independents. [By religious Americans, I mean those who responded that religion was important to them] Show your work, specify what the null hypothesis is, and say whether or not you can reject the null hypothesis with 95% confidence.

c. Perform a chi-square test to assess whether the relationship between religiosity and partisanship is statistically significant. Show your work. Specify what the null hypothesis is, what the chi-square statistic is, and whether or not you can reject the null hypothesis with 95% confidence.

Answer 1

Null hypothesis, H0: No relationship between religiosity and partisanship

Alternative hypothesis, H1: H0 is not true.

Observed frequencies:

	Religion Not Important	Religion Important	Total
Democrat	130=O11	220=O12	350=O10
Independent	85=O21	255=O22	340=O20
Republican	35=O31	275=O32	310=O30
Total	250=O01	750=O02	1000=N

Expected frequencies:

	Religion Not Important	Religion Important
Democrat	87.5=e11	262.5=e12
Independent	85=e21	255=e22
Republican	77.5=e31	232.5=e32

Since p-value<0.05 so we reject H0 at 5% level of significance and conclude that relationship between religiosity and partisanship is significant.