Question

Each year over 1,000 college students die in alcohol-related deaths, often in cases that involve binge drinking. Harvard School of Public Health reported in 2004 that 44% of college students are binge drinkers. In an informal anonymous survey conducted in a statistics class shortly after the Harvard report was released, students were asked: "In the past two weeks, have you had (males) more than five alcoholic drinks on one occasion? (females) more than four alcoholic drinks on one occasion?" [This is how experts classify a student to be a binge drinker or not.] Suppose the proportion answering yes was 29/68 = 0.43.

(a) Report the center of the distribution of sample proportion, when population proportion is 0.44 and sample size is 68. (Round your answer to two decimal places.)

Report the spread of the distribution of sample proportion, when population proportion is 0.44 and sample size is 68. (Round your answer to two decimal places.)

How can we characterize the shape of the distribution?

approximately normal
unknown
skewed right
skewed left

(b) How usual or unusual is a sample proportion as low as 0.43 in this situation?
not at all unusual
fairly unusual
extremely unusual

Answer 1

Solution:

a. The center of the distribution of sample proportion is population proportion, p = 0.44

The spread of the distribution of sample is the standard error, Se = $\sqrt{p(1-p)/n)}$ = $\sqrt{0.44(1-0.44)/68)}$ =0.0602

The shape of the distribution is approximately normal.

b. The sample proportion is not at all unusual because the probability is greater than or equal to this simple proportion is greater than 5%.