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 (????????
) 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?
inions about an upcoming building project, the college president wishes to obtain a simple random sample of 8
students. He numbers the students from 1 to 7663
Complete parts (a) and (b) below.
Click the icon to view the random number table.
(a) Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 2, column 4. Using this position as the starting point and proceeding downward, determine the numbers for the 8
students who will be included in the sample.
rd deviation of $17,093. We are interested in the true average college tuition in the U.S.
a. What parameter are we estimating?
b. What is the point estimate of that parameter?
c. Build the margin of error for 95% confidence interval for the true average college tuition in the U.S. (Show work for credit)
d. Using your answer in part c, build a 95% confidence interval for the true average college tuition in the U.S.
e. Interpret your interval in part d.