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 12,611 students in 1993 and 8,568 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 (0.083 , 0.107).

(a) The difference between the proportions in 2001 and 1993 is  . The proportion appears to have  
---Select---

decreased

stayed the same

increased
between 1993 and 2001.

(b) Given the standard error for these data is 0.007 , which is correct?
Standard error is the standard deviation of the population distribution of the difference between the sample proportions.Standard error is the standard deviation of the sampling distribution of the difference between the sample proportions.     Standard error is the standard deviation of the sampling distribution of the sample proportions.
(c) What is the interpretation about whether or not the confidence interval contains 0?
It does contain zero, which is not evidence of an increase in reports of "getting drunk" as an important reason.It does contain zero, which is evidence of an increase in reports of "getting drunk" as an important reason.     It does not contain zero, which is not evidence of an increase in reports of "getting drunk" as an important reason.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?
The interval is narrow because the difference between proportions is small.The interval is narrow because the standard error is large, which is because the sample sizes are large.     The interval is narrow because the difference between proportions is large.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.
data quantitativesamples dependent and obtained systematicallysamples independent and obtained randomlydata categoricalsufficiently large sample sizes

Explanation / Answer

Answers:

Part a

The difference between the proportions in 2001 and 1993 is increased between 1993 and 2001.

(Explanation: The confidence interval (0.083, 0.107) does not contain the value 0 and confidence interval only indicates the positive values. This means differences in population proportions are positive. So, difference between the proportions in 2001 and 1993 is increased between 1993 and 2001.

Part b

Answer:

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

(Explanation: For the given scenario, we are dealing with the variable difference between the two population proportions for the year 1993 and 2001. For this scenario, the population parameter is difference between population proportions. So, standard error is nothing but the standard deviation of the sampling distribution of the difference between the sample proportions.)

Part c

Answer:

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

(Explanation: The confidence interval (0.083, 0.107) does not contain the value 0 and confidence interval only indicates the positive values. Positive values suggests increase in reports of "getting drunk" as an important reason.)

Part d

Answer:

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

(Explanation: We know that as we increase the sample size, the width of the confidence interval decreases. For the given scenario, the sample size is comparatively very large and that’s why the standard error is small which results in narrow confidence interval.)

Part e

Assumptions:

Samples used for the year 1993 and year 2001 are independent because researcher uses different samples for these two years.

Data used in the survey is categorical data. The categorical variable used is ‘whether student feels that “to get drunk” is important reason for drinking alcohol.

Large sample sizes were used for this research study.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.