Question

The Pew Research Center conducted a poll from April 29-May 5, 2020. I’ve rounded some numbers to make the math easier, but the results are basically the same as what they got. There were 10,000 US adults in the sample, and they asked them if they were Democrat/Lean Democrat or Republican/Lean Republican. They also asked them to fill in the blank in the following sentence: “There should be ____ restrictions on public activity because of the outbreak in my area." Possible choices for the blank were: More, About the same as now, or Fewer. Out of the 10,000 respondents, 4200 said they were Republican/Lean Republican, and 5800 said Democrat/Lean Democrat. Out of the Republicans, 16% favored more restrictions, 40% same, 44% less. For the Democrats, 35% said more, 57% same, and 8% less. You can assume the data come from a simple random sample with no bias of any kind. Do a hypothesis test (using the full outline form) to see if political party affiliation and opinion about restrictions are independent.

Answer 1

observed	Rebuplican	Democrat	Total
More	672	2030	2702
Same	1680	3306	4986
Less	1848	464	2312
Total	4200	5800	10000

Here we create a contingency table for the col heads being the party and the row being the proportion of favorable number of restrictions.

The total for columns hve been provided 4200 and 5800. For the restrictions percentages are given. So multiplying those with corresponding total party we get individual cell values.

We want conduct a hypothesis test to see if political party affiliation and opinion about restrictions are independent.So we use a chi-square table. For that we also need the expected values.

The expected value for each cell is found by

Row total * col total/ overall total

Expected	Rebuplican	Democrat	Total
More	1134.84	1567.16	2702
Same	2094.12	2891.88	4986
Less	971.04	1340.96	2312
Total	4200	5800	10000

	Rebuplican	Democrat
More	188.767	136.694
Same	81.894	59.302
Less	791.995	573.514

Test

Null: Political party affiliation and opinion about restrictions are independent.

Alternative:Political party affiliation and opinion about restrictions are not independent.

Chi -square test STat =

Test Stat = 1832.166

df = (r -1) * (c -1) ...................... r = no. of rows and c = no. of columns

  = 2 * 1

df = 2

level of significance = 0.05 ..............can be of choice

C.V. =

=   

Critical value = 5.991   ..................we use chi-square probabiltiy ditribution tables for it.

Since |Test Stat| > C.V.

We reject the null hypothesis at 0.05 level. We conclude that political party affiliation and opinion about restrictions are not independent significantly.