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 beginning of February, 2021, President Biden's approval rating was reported to be 56%, while at the beginning of March, 2021, it was reported to be 54%.

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?

(a) State the null hypothesis and alternative hypothesis in terms of the original problem. (Remember, hypotheses should be statements about population parameters.)

Null:

Alternative:

(b) Under the null hypothesis, the difference in the percentages is expected to be________%. The estimated standard error for this difference is ________%.

(c) The two-sample z test statistic is __________.

(d) The p-value = _________%.

(e) Our conclusion is (circle one)...

reject the null hypothesis OR don't reject the null hypothesis.