Based on your answer in part e, does the president's claim seem believable?

In practice, parts e and f would be the last things you would do in your own study. But, let's do one more thing, even though it takA college president claims that 24.5% of the students support his decision to shut down a department. So, you take an SRS of 200 students from the college's 15,000 students, and find that 66 students support the president's decision.

a) Explain in words what proportion it is that we are truly interested in.

b) What's the sample size? Make sure you get this right, otherwise all of your answers will be wrong.

c) Find the sample proportion p_hat.

d) Find the 95% CI for the population proportion p. Report it both as (something plus/minus something) and as an interval [something, something].

e) Explain/Interpret the [something, something] CI found in part d, in two ways: In the first way use the word "proportion," and es us backward in the flow of the lecture. This next question is important not only for reinforcing what we studied in the lecture, but also because it sets the stage for something else that we will study later (something related to a "p-value.").

g) Suppose the president is correct in his claim. Find the probability that a random sample proportion p_hat, from a random sample of size found in part b, will be between 0.2 and 0.29 (i.e., between 20% and 29%). To that end,

- Find the mean and standard deviation of the sampling distribution of p_hat, (to make the math simpler, find the standard deviation to 3 decimal places).