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?

skewed left, approximately normal, skewed right, unknown

(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

A)

Center of distribution is population proportion = 0.44

Spread = √{p*(1-p)}/√n = √{0.44*(1-0.44)/68} = 0.06019575908

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 29.92

N*(1-p) = 38.08

Both the conditions are met so we can use standard normal z table to estimate the probability.

Answer is normal.

B)

Z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 0.43

Claimed P = 0.44

N = 68

After substitution.

Z = -0.17

From z table, P(z<-0.17) = 0.4325

Since probability is greater than 0.05.

It is not at all unusual.