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). Researchers randomly sampled 12,282 students in 1993 and 8,636 students in 2001. Students were asked if they feel that "to get drunk" is an important reason for drinking alcohol. A 90% confidence interval for the difference in the proportion (p2001 - p1993) that feel "to get drink" is an important reason for drinking alcohol is (0.090 , 0.114).

(a) The difference between the proportions in 2001 and 1993 is _____. The proportion appears to have _____(increased/decreased) between 1993 and 2001.

(b) Given the standard error for these data is 0.007 , which is correct?

A) Standard error is the standard deviation of the sampling distribution of the difference between the sample proportions.

B) Standard error is the standard deviation of the sampling distribution of the sample proportions.

C) Standard error is the standard deviation of the population distribution of the difference between the sample proportions.

(c) What is the interpretation about whether or not the confidence interval contains 0?

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

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

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

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

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

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

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

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

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

(e) State and check the assumptions for the confidence interval in (c) to be valid.

A) sufficiently large sample sizes

B) data categorical

C) samples dependent and obtained systematically

D) data quantitative

E) samples independent and obtained randomly

Explanation / Answer

a)The difference between the proportions in 2001 and 1993 is (0.09+0.114)/2=0.102 The proportion appears to have

increased between 1993 and 2001.

b)A) Standard error is the standard deviation of the sampling distribution of the difference between the sample proportions.

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

d)

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

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