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.

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.

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 =

                         =

                         =

                          =

                          = 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.

answer: 25 is the correct answer

step-by-step explanation: