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Fox news recently reported the results of a public opinion poll on supporting trump that asked since he became the president


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1.Fox News recently reported the results of a public opinion poll on supporting Trump that asked: “Since he became the president, ...

Since he became the president, did President Trump act with the transparency and the integrity that you expect from a president?” 675 voters responded the poll and 351 responded “YES.” Assume that 40% of the U.S. population supports Trump. a. Define a binary random variable, Y, for supporting Trump (Y=1) vs. not (Y=0). Calculate the population mean (????????) and variance (???????? 2 ) for supporting Trump. b. Calculate the sample mean ????̅ and the sample standard deviation of ????̅ (????????̅ ) for the poll. c. Calculate the standard error of ????̅ and construct a 95% confidence interval from the poll using ????̅ and its sample standard error. d. Conduct a two-sided hypothesis test at 5% significance level to determine whether 40% of the U.S. population supports Trump. State the null and the alternative hypotheses, calculate the test statistics and the associated p-value, and conclude. Is the Fox News survey reliable? Why? Why Not? e. Suppose that you wanted to design a survey that had a margin of error of at most 1%. That is: the difference between the upper bound and the lower bound of the confidence interval should be a maximum of 2 percentage points. For example, for ????̅ = 0.52 you are aiming for the 95 % CI to be [0.51 0.53]. How large should n be if the survey uses simple random sampling?
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