Gambling is an issue of great concern to those involved in intercollegiate athle

Question

Gambling is an issue of great concern to those involved in intercollegiate athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed student-athletes concerning their gambling-related behaviors*. Of 5594 Division I male athletes surveyed, 3547 reported participation in some gambling behavior; of 3469 Division I female athletes surveyed, 1447 reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities.

Perform a hypothesis test to determine if there is a difference in the proportions of Division I male and female student-athletes who participate in gambling behavior. Let pm and pf be the proportion of all Division I male and female athletes, respectively, who participate in gambling behavior. Calculate sample proportions to 3 decimal places; calculate the standard error to 5 decimal places.

Question 1. Calculate the value of the test statistic for this hypothesis test.
1


Question 2. If the significance level = .05 is used, what is the rejection region for this hypothesis test?
z < 2 lower bound

Explanation / Answer

Let p1 be the proportions for men

p2 be the proportions for women

p1=3547/5594=0.63
p2= 1447 /3469=0.42

Question1:

The test statistic is

Z=(p1-p2)/v[p1*(1-p1)/n1+p2*(1-p2)/n2]

=(0.63-0.42)/sqrt(0.63*(1-0.63)/5594 + 0.42*(1-0.42)/3469)

=19.85

Question 2:

Given a=0.05, the rejection region is Z<-1.96 or Z>1.96

Question 3:

Reject H0 and conclude that the proportions of male and female Division I athletes that particpate in gambling behavior are different.

Question 4:

Given a=0.05, |Z(0.025)|=1.96 (from standard normal table)

So 95% CI is

(p1-p2)+/- Z*v[p1*(1-p1)/n1+p2*(1-p2)/n2]

--> (0.63-0.42) +/- 1.96*sqrt(0.63*(1-0.63)/5594 + 0.42*(1-0.42)/3469)

--> (0.1892673, 0.2307327)

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