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?