Question

Let's say you want to poll a random sample of 150 students on campus to see if they prefer to take online classes. Of course, if you took an actual poll you would only get one number (your sample proportion, p-hat). Imagine all the possible samples of 150 students that you could draw and the distribution of all the possible sample proportions you would get from them. If I told you that we know that 35% of all students actually prefer to take classes online, how would you respond to the following?:

1. Discuss the conditions necessary to use the normal curve to model this sampling distribution and explain whether or not they are met.

2. If the normal model is appropriate for this distribution, what shape would you expect it to have?

3. If you were to use the normal model for this p-hat sampling distribution, what value would be at the center of your sampling distribution? In other words, what value would all of those sample proportions center around?

4. What would be the standard deviation of this sampling distribution?

Answer 1

1) n = 150

p = 0.35

np = 150 * 0.35 = 52.5

n(1 - p) = 150 * (1 - 0.35) = 97.5

Since np > 10 and n(1 - P) > 10 , so we can use normal approximation.

2) It would be the bell-shaped.

3) = p = 0.35

4) = sqrt(p(1 - p)/n)

= sqrt(0.35 * (1 - 0.35)/150)

= 0.0389