Question 993868: I'm not sure if this is the right place to post this but I'm pretty stuck. I'm having a hard time understanding how to do this or what I even need to do. Any help would be much appreciated.
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). But, imagine all the possible samples of 150 students that you could draw and the imagined histogram of all the sample proportions from those samples.
1. What shape would the histogram of all the possible sample proportions (p-hat's) have?
2. Where would the center of that histogram be? (This answer should be a description in words based on what we know about p-hat sampling distributions.)
Now, given the information that about 35% of students actually prefer to take classes online respond to the following:
3. Discuss the conditions necessary to use the normal model here and explain whether or not they are met.
4. If you were to use the normal model for this p-hat sampling distribution, what would be the parameters (mean and standard deviation) for your model?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! A short discussion of p^ relative to this problem. The p^ symbol is used to refer to a proportion of the sample of the entire group. In this problem p^ would refer to the proportion of the sample group that prefer to take online classes.
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1) Histogram will approximate a bell (normal) probability curve.
2) The mean of the sampling distribution is equal to the mean of the population.
3) In practice, a sample size of 30 is large enough when the population distribution is roughly bell-shaped. Our sample size is 150 so this meets the constraint and the histogram approximates a normal(bell) probability curve.
4) P = 0.35, Q = 0.65, n = 150, then
mean = 150 * .35 = 52.5
std.dev. = square root( (0.35*0.65) / 150 ) = 0.038944405
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