Random samples of students at 107 four-year colleges were interviewed several times since 1998. Of the students who reported drinking alcohol, the percentage who reported bingeing at least three times within the past two weeks was 41.1% of 336 students in 1998 and 21.6% of 843 students in 2004. a. Estimate the difference between the proportions in 2004 and 1998, and 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.

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Random samples of students at 107 four-year colleges were interviewed several times since 1998. Of the students who reported drinking alcohol, the percentage who reported bingeing at least three times within the past two weeks was 41.1% of 336 students in 1998 and 21.6% of 843 students in 2004.

a. Estimate the difference between the proportions in 2004 and 1998, and 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.

B. The proportion of the student population in 1998 who reported drinking alcohol that binged at least three times within the past two weeks.

D. The proportion of the student population in 2004 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 1998 to 2004. 

(Round to three decimal places as needed.)
Transcribed Image Text:Random samples of students at 107 four-year colleges were interviewed several times since 1998. Of the students who reported drinking alcohol, the percentage who reported bingeing at least three times within the past two weeks was 41.1% of 336 students in 1998 and 21.6% of 843 students in 2004. a. Estimate the difference between the proportions in 2004 and 1998, and 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. B. The proportion of the student population in 1998 who reported drinking alcohol that binged at least three times within the past two weeks. D. The proportion of the student population in 2004 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 1998 to 2004. (Round to three decimal places as needed.)
Expert Solution
Step 1: Write the given information.

table row cell p with hat on top subscript 1998 end cell equals cell 0.411 end cell row cell n subscript 1998 end cell equals 336 row cell p with hat on top subscript 2004 end cell equals cell 0.216 end cell row cell n subscript 2004 end cell equals 843 end table

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