Question

The PACE project (pace.uhs.wisc.edu) at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on the random sample, the percentage of UW students who reported binge drinking at least three times within the past two weeks was 42.2% in 1999 and 21.2 % in 2009. You want to test if this is a significant decrease.

Answer 1

Question:

The question is incomplete. The value of n and the required calculation was not given. Below is the remaining part of the question.

In 1999, n = 334

In 2009, n = 843

1   Estimate the difference between the proportion in 1999 and 2009

2. Find the standard error of this difference.

3. Construct and interpret a 95% confidence interval to estimate the true change, explaining how our interpretation reflects whether the interval contains 0.

Answer:

1. Difference between the proportion = 0.21

2. Standard error = 0.030471

3. There is a significant decrease.

Step-by-step explanation:

Given data:

Year                                 1999                       2009

Sample size                  n1 = 334                   n2 = 843

Sample proportion        p1= 0.422                p2 = 0.212

1. The difference between the proportion is calculated as;

Difference = p1 -p2

                  = 0.422 - 0.212

                   =0.21

2. Calculating the standard error using the formula;

Standard error = $\sqrt{\frac{p1(1-p1)}{n1}+ \frac{p2(1-p2)}{n2} }$

                         = $\sqrt{\frac{0.4422(1-0.422)}{334}+\frac{0.212(1-0.212)}{843} }$

                         = $\sqrt{0.00073 + 0.000198}$

                          =$\sqrt{0.000928}$

                          = 0.030471

Therefore, the standard error = 0.030471

3. Calculating 95% confidence interval using the formula;

95% confidence interval = p1-p2 ±Za (SE(p1-p2))

                                         = 0.422 - 0.212 ± 1.96*0.030471

                                         = 0.21 ±0.059722

                                        = 0.1503, 0.2697

        0.1503 ≤ (p1-p2) ≤ 0.2697

The 95% confidence interval is (0.1503, 0.2697). The value 0 is not included in the 95% confidence interval. Hence, we may conclude that the students of Wisconsin binge at least three times in the past two weeks in the year 1999 and 2009 has been decreased.