Question

I mostly need help with question 2(I put Q1 on here for reference)

1. The Gallup organization periodically polls adults living in the U.S. about their approval or

disapproval of the job the President of the U.S. is doing. At the end of President Trump’s first

month in office, January 2017, his approval rating was 45%, while at the end of last month,

March, 2020, his approval rating was 49%.

For the purpose of this problem, suppose that the sample size was 200 in both months, that

each represented a simple random sample of adults living in the U.S. at that time, and that the

two samples were chosen independently of each other. Is there evidence for a real change in

opinion among U.S. adults, or could this result be due just to chance?

2. Consider the same setup as in problem 1, but suppose the participants who were randomly

selected in March, 2020 were also asked whether they approved of the job being done by U.S.

Speaker of the House, Nancy Pelosi, and the percentage was 39%.

Would it be appropriate to use the sample values of 49% and 39% to construct a two-sample z

test statistic, as we did in problem 1, for the null hypothesis that the approval ratings between

President Trump and Speaker Pelosi were the same in March, 2020?

YES or NO (circle one)

Explain your answer:

Answer 1

Answer

NO

In this case, the best option is to use the sample values of 49% and 39% to construct a Z test for paired samples, since the two questions are asking over the same individual, therefore, this advantage can be used to decrease the variability of the estimations.