Question

The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performance-enhancing drugs are a problem in college sports?" Suppose that 30% of all Division I athletes think that these drugs are a problem. Let p^ be the sample proportion who say that these drugs are a problem.
Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p^?

a) Mean = 0.30, SD = 0.017
b) Mean = 0.30, SD = 0.55
c) Mean = 0.30, SD = 0.0003
d) Mean = 225, SD = 12.5
e) Mean = 225, SD = 157.5

Answer 1

Answer:

a) Mean = 0.30, SD = 0.017

Step-by-step explanation:

The mean and sampling distribution of the sample proportion can be found using the equations

Mean= p

$SD=\sqrt{\frac{p*(1-p)}{n} }$

where

• n is the sample size (750)

• p is the sample proportion of all Division I athletes think that these drugs are a problem (0.30 or 30%)

Using these information:

Mean = 0.30

$SD=\sqrt{\frac{0.30*0.70}{750} }$ ≈ 0.017