Let\'s say you want to poll a random sample of 150 students on campus to see if

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). 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?

Explanation / Answer

1) the shpae of all the possible sample proportions would be approximately normal as per central limit theorum

2)center of the histogram will be at population proportion p.

3) as for normal model np and n(1-p) should be greater then 10.

here n=150 and p=0.35

hence np>52.5 and n(1-p)=97.5 both are greater then 10 therefore conditions are met.

4) mean of phat sampling distribution =p=0.35

and std deviaiton =(p(1-p)/n)1/2 =0.0389

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