1. The Gallup organization periodically polls adults living in the US. about their approval or disapproval ofthe 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 November, 2021, it was reported to be 42%. For the purpose of this problem, suppose that the sample size was 150 in both months, that each represented a simple random sample of adults living in the US. at that time, and that the two samples were chosen independently of each other. Is there evidence for a real change in opinion among US. 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, these should be statements about population parameters.) (b) Under the null hypothesis. the difference in the percentages is expected to be \"lo. The estimated standard error for this difference is "2%. (c) The tw'o-sample 2 test statistic is (d) The p-value = %. (e) Our conclusion is (circle one) reject the null hypothesis 0R don't reject the null hypothesis. 2. Under the same setup as #1, suppose the Gallup organization asked the same survey participants in November, 2021 if they approved of the job being done by Vice President Kamala Harris, and 49% said they approved. Would it be appropriate to can'y out the same steps as in #1 to evaluate the evidence for whether Biden and Han'is had the same approval rating among the US. population in November, 2021? Why or why not? 3. The p-value of a two-sample 2 test turns out to be about 8%. using a two-sided altemative hypothesis. Which, if any, of the following are correct statements about the p-value? (circle them) (a) The null hypothesis is true. (b) The null hypothesis has an 8% chance of being true. (c) The alternative hypothesis is true. (d) The altemalive hypothesis has an 8% chance of being true. (e) The test is statistically signicant. (1} If the null hypothesis is true, two in twenty ve random samples would produce a result like ours or something even more extreme. (g) If we had can'ied out a one-sided test instead, the test would have been statistically signicant