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)

symmetric and have bell-shaped density curves with a single peak.

2)

center would be p^ (Sample proportion)

X/n

3)

condition to be met

np > 5 , nq >5

here np = 150 *0.35 > 5

nq = 150 * 0.65 > 5

hence conditions are met

4) mean = p^ = 0.35

sd =sqrt(pq/n) = sqrt(0.35*0.65/150) = 0.0389444

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.