Question

Random samples of students at 122 ​four-year colleges were interviewed several times since 1995. Of the students who reporteddrinking alcohol the percentage who reported bingeing at least three times within the past two weeks was 41.4​% of 333 students in 1995 and 21% of 841 students in 2007

a. Estimate the difference between the proportions in 2007and 1995​, interpret.

b. Find the standard error for this difference. Interpret it.

c. Define the two relevant population parameters to compare in the context of this exercise.

d. Construct and interpret a 90​% confidence interval to estimate the true difference

e. State the assumptions for the confidence interval in part d to be valid.

a. Estimate the difference between the proportions in 2007 and 1995. ​(Round to three decimal places as​ needed.) Interpret this estimate. Choose the sentence below that best describes the difference

A.The proportion appears unchanged from

B.The proportion appears to have decreased

C.The proportion appears to have increased

D.The proportion appears to have changed from but it is not possible to tell if it has increased or decreased.

b. What is the standard error for this​ difference?Interpret this value.

The standard error is the estimated ---- of the ---- for the difference between the sample ----

c. What are the two relevant population parameters to compare in the context of this​ exercise? Select all that apply.

A.The number of students in the 1995 population in who reported drinking alcohol that binged at least three times within the past two weeks.

B.The proportion of the student population in 1995 who reported drinking alcohol that binged at least three times within the past two weeks.

C.The number of students in the population in 2007who reported drinking alcoholthat binged at least three times within the past two weeks.

D.The proportion of the student population in 2007 who reported drinking alcohol that binged at least three times within the past two weeks.

d. Construct a 90​% confidence interval for the difference between the population proportions from 1995 to 2007 ​(Round to three decimal places as​ needed.)

Interpret the 90​% confidence interval.

There ---- evidence that the true proportion --- from 1995 to 2007 because the interval ---- 0.

e. What assumptions are necessary for the confidence interval to be​ valid?

A.The response variable is​ categorical, and both samples must be selected from a population that is approximately normal.

B.The response variable is​ categorical, and both samples must be independent and p1 must be close to p2.

C.The response variable is​ quantitative, and both samples must include the same students.

D.The response variable is​ categorical, and both samples must be​ independent, random, and large enough.

Answer 1