Question

A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

Questions 1 - 6 pertain to scenario 1.

Question 1 (1 point)

Which of the following properly explains the 95% confidence interval for the true proportion of the professor's students who were registered to vote?

Question 1 options:

	a) We are 95 % confident that between 57.3% and 82.7% of the professor's students are registered to vote.
	b) We are 95% confident that at least 57.3% of the professor's students are registered to vote.
	c) We are 95% confident that less than 80.69% of the professor's students are registered to vote.
	d) We are 95 % confident that between 59.3% and 80.69% of the professor's students are registered to vote

Question 2 (1 point)

Explain what 95% confidence means in this context.

Question 2 options:

	a) If samples of students with grades higher than a B average were taken, 9% of the confidence intervals produced would contain the actual percentage of the professor's students who are registered to vote.
	b) If many random samples were taken, 95% of the confidence intervals produced would contain the actual percentage of the professor's students who are registered to vote.
	c) 95% of the students would have to be sampled to find the actual percentage of the students who are registered to vote.
	d) 5% of the students would have to be samples to find the actual percentage of the students who are registered to vote.

Question 3 (1 point)

What would your response be if you were asked by a non-statistical student about the probability that the true proportion of the professor's students who were registered to vote is in your confidence interval?

Question 3 options:

	a) You would tell the student that identifying the probability would be impossible since there was not enough information to construct the interval of students registered to vote.
	b) You would tell the student that the probability would likely be 95% since the confidence interval relates to the percentage of student that a truly registered to vote.
	c) You would tell the student that the probability would be approximately 5% since the true interval of students registered to vote is equal to (1 - confidence interval).
	d) You would tell the student that there is no probability involved. Once the interval is constructed the true proportion of the professor's students registered to vote is either in the interval or is not in the interval.

Question 4 (1 point)

According to a Gallup poll, about 73% of 18- to 29-year-olds said that they were registered to vote. How would you interpret the Gallup poll's result?

Question 4 options:

	a) The figure from the Gallup poll seems reasonable since 73% lies in the confidence interval.
	b) The figure from the Gallup poll in unreasonable since 73% lies outside of the confidence interval.
	c) No interpretation can be made about the Gallup poll since the confidence level was not stated.
	d) No interpretation can be made since you are not told the sample size used by the Gallop poll.

Question 5 (1 point)

If the professor only knew the information from the Gallup poll and wanted to estimate the percentage of her students who were registered to vote to within ±4% with 95% confidence, what approach would she use to determine how many students she should sample?

Question 5 options:

	a) She would use the margin of error formula with a margin of error of 1%.
	b) She would use the margin of error formula with a margin of error of 9%.
	c) She would use the margin of error formula with a margin of error of 4%.
	d) Should would use the margin of error formula with a margin of error of 5%.

Question 6 (1 point)

Suppose the professor wanted to make the margin of error smaller. What would accomplish this?

Question 6 options:

	a) Increase the level of confidence
	b) Increase the population size
	c) Decrease the level of confidence
	d) Decrease the population size

Answer 1

Here

Sample size = n = 50

Number of students  registered to vote = 35

So,

proportion of the professor's students who were registered to vote is

For 95%, the z-value is 1.96

Now

95% confidence interval for true proportion is

  

( 0.573 , 0.827)

Therefore, the correct option is

a)	We are 95 % confident that between 57.3% and 82.7% of the professor's students are registered to vote.

2)

The correct option is

b)	If many random samples were taken, 95% of the confidence intervals produced would contain the actual percentage of the professor's students who are registered to vote.

3)The correct option is

d)	You would tell the student that there is no probability involved. Once the interval is constructed the true proportion of the professor's students registered to vote is either in the interval or is not in the interval.

4)

The 95% confidence interval for true proportion is ( 0.573 , 0.827)

i,e between 57.3% and 82.7%

Therefore,

The correct option is

a) The figure from the Gallup poll seems reasonable since 73% lies in the confidence interval.

5)

The formula for margin of error for proportion is

by putting

M.E = 4% = 0.04

Z = 1.96 ( for 95% Confidence interval)

= 73% = 0.73 (according to a Gallup poll )

you can find the value of n

The correct option is

c)	She would use the margin of error formula with a margin of error of 4%

6)

The formula for margin of error for proportion is

The "Z" value for Confidence Interval here:

Confidence Level	Z
80%	1.282
85%	1.440
90%	1.645
95%	1.960
99%	2.576
99.5%	2.807
99.9%	3.291

Margin of error is directly proportional to the confidence level.

In order to decrease the margin of error, you can either decrease the confidence level or increase the sample size.

The correct option is

c)	Decrease the level of confidence