Gambling is an issue of great concern to those involved in i

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. 1380 out of a total of 3361 female student-athletes reported participation in some gambling activity.

(a) Use the large-sample methods to find an estimate of the true proportion with a 99% confidence interval.

(b) The margin of error for this sample is not the same as the margin of error for male athletes. There were 5594 males in the study, and p? was found to be 0.6341. Explain why the margin of error differs.

A. The margin of error for males is smaller because the sample size is smaller.

B. The margin of error for males is larger because p? is larger.    

C. The margin of error for males is smaller because the sample size is larger.

D. The margin of error for males and females are the same.

Solution

A)

p=1380/3361=0.41

z_c = 2.58         and     n = 3361

0.41+-2.58[(0.41)*(0.59)/3361]^1/2

0.41+-0.02       

Hence we can conclude that between 39 and 43 percent

Lower limit 39%

Upper limit 43%

B)