The College Alcohol Study at the Harvard School of Public Health has interviewed

Question

The College Alcohol Study at the Harvard School of Public Health has interviewed random samples of students at 119 4-year colleges several times since 1993 (see Journal of American College Health, vol. 50, pp. 203-217, 2002). Of the students who reported drinking alcohol, the percentage who reported that drinking "to get drunk" is an important reason for drinking was 35.3% of 12,329 students in 1993 and 47% of 8602 students in 2001.

1) Construct and interpret a 90% confidence interval to estimate the true difference in proportions, explaining how your interpretation reflects whether the interval contains 0.

2) Choose:

a)It does contain zero, which is evidence of an increase in reports of "getting drunk" as an important reason.

b)It does contain zero, which is not evidence of an increase in reports of "getting drunk" as an important reason.     

c)It does not contain zero, which is evidence of an increase in reports of "getting drunk" as an important reason.

d)It does not contain zero, which is not evidence of an increase in reports of "getting drunk" as an important reason.

3) What is the main factor that causes the confidence interval to be so narrow?

a)The interval is narrow because the standard error is large, which is because the sample sizes are large.

b)The interval is narrow because the difference between proportions is small.     

c)The interval is narrow because the standard error is small, which is because the sample sizes are large.

d)The interval is narrow because the difference between proportions is large.

4) State and check the assumptions for the confidence interval in (3) to be valid.

a) samples dependent and obtained systematically

b) samples independent and obtained randomly

c) sufficiently large sample sizes

d) data categorical

e) data quantitative

Explanation / Answer

proprotion who reported that drinking in 1993=p1=0.35 and its sample size=n1=12329

proprotion who reported that drinking in 2001=p2=0.47and its sample size=n2=8602

difference of proprotion=absolute(p1-p2)=absolute(0.35-0.47)=0.12

SE(p1-p2)=sqrt(p1(1-p1)/n1+p2(1-p2)/n1)=sqrt((0.35*(1-0.35)/12329)+(0.47*(1-0.47)/8602))=0.0069

(answer1)(1-alpha)*100% confidence interval for (p1-p2)=(p1-p2)±z(alpha/2)*SE(p1-p2)

90% confidence interval =0.12±z(0.1/2)*0.0069=0.12±1.6449*0.0069=0.12±0.0113=(0.1087, 0.1313)

(answer 2) right choice is

(a)It does contain zero, which is evidence of an increase in reports of "getting drunk" as an important reason.

(answer 3) right choice is

c)The interval is narrow because the standard error is small, which is because the sample sizes are large.

(answer 4) right choices are

b) samples independent and obtained randomly

c) sufficiently large sample sizes

d) data categorical

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