Question

1- The PACE project at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two weeks was 42.2% in 1999 (n = 334) and 21.2% in 2009 (n = 843). Test that the proportion of students reporting bingeing in 1999 is different from the proportion of students reporting bingeing in 2009 at the 10% significance level.

(A) What are the null and alternative hypotheses?

(B) Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?

(C.1) Calculate the appropriate test statistic, showing your work.

(C.2) Calculate the appropriate test statistic, showing your work.

(D) Calculate the corresponding p-value from the appropriate table

(E) What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Group of answer choices.

(F) Which conclusion is true according to your results?

a) |zcalc|>|zcrit|andp<α|zcalc|>|zcrit|andp<α

Thus I can reject the plausibility of zero for the true difference in proportions of UW students reporting bingeing at least three times per week in 1999 and 2009 in the population and can conclude that the true difference in proportions of UW bingers between 1999 and 2009 is statistically significantly different from zero at the 10% significance level.

b) |zcalc|<|zcrit|andp<α|zcalc|<|zcrit|andp<α

Thus I can reject the plausibility of zero for the true difference in proportions of UW students reporting bingeing at least three times per week in 1999 and 2009 in the population and can conclude that the true difference in proportions of UW bingers between 1999 and 2009 is statistically significantly different from zero at the 10% significance level.

c) |zcalc|>|zcrit|andp>α|zcalc|>|zcrit|andp>α

Thus I can not reject the plausibility of zero for the true difference in proportions of UW students reporting bingeing at least three times per week in 1999 and 2009 in the population and can conclude that the true difference in proportions of UW bingers between 1999 and 2009 is statistically significantly different from zero at the 10% significance level.

d) |zcalc|<|zcrit|andp>α|zcalc|<|zcrit|andp>α

Thus I can not reject the plausibility of zero for the true difference in proportions of UW students reporting bingeing at least three times per week in 1999 and 2009 in the population and can conclude that the true difference in proportions of UW bingers between 1999 and 2009 is statistically significantly different from zero at the 10% significance level.

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