Question 1

Which of the following statements correctly describes a point estimate for a population proportion?

Accepted Answer

A point estimate is a single value, such as the sample proportion $$\hat{p}$$, used to estimate the population proportion $$p.$$

Question 2

In a survey of 950 undergraduate students, 53% reported taking online courses. What is the best point estimate of the proportion of all undergraduate students who take online courses?

Accepted Answer

$$0.53$$

Question 3

Which of the following is NOT a requirement for constructing a confidence interval for a population proportion $$p$$?

Accepted Answer

The population size must be at least 10 times the sample size.

Question 4

What is the correct interpretation of a 95% confidence interval $$0.405 \u003c p \u003c 0.455$$ for a population proportion?

Accepted Answer

We are 95% confident that the interval from $$0.405 to$$ $$0.455$$ actually does contain the true value of the population proportion $$p.$$

Question 5

Given a sample proportion $$\hat{p}$$, sample size $$n$$, and a critical value $$z_{\alpha/2}$$, which formula gives the margin of error $$E$$ for estimating a population proportion?

Accepted Answer

$$E = z_{\alpha/2} \sqrt{\dfrac{\hat{p}\hat{q}}{n}}$$

Question 6

A 2016 Pew Research Center survey found that 79% of 4787 adults shop online. If you want to be 95% confident that your sample percentage is within 3 percentage points of the true proportion, and you have no prior estimate for $$p$$, what sample size $$n$$ should you use?

Accepted Answer

$$n = \dfrac{[z_{\alpha/2}]^2 \cdot 0.25}{E^2$}$$

Question 7

If the computed sample size for a survey is $$708.135$$, what should you do according to the round-off rule for determining sample size?

Accepted Answer

Round up to $$709.$$

Question 8

Which method for constructing a confidence interval for a population proportion is considered best as a teaching tool for introducing students to confidence intervals?

Accepted Answer

Wald confidence interval

Question 9

A medical study reports that 70% of 71 subjects were abstinent from smoking at 8 weeks, with a 95% confidence interval of 58% to 81%. What is the margin of error $$E$$?

Accepted Answer

$$E = 0.115$$

Question 10

Which of the following statements about the effect of population size on the reliability of poll results is correct?

Accepted Answer

The population size is usually not a factor in determining the reliability of a poll.

Question 11

Which confidence interval method is described as 'exact' and is based on the binomial distribution, but is criticized for being too conservative?

Accepted Answer

Clopper-Pearson method

Question 12

What is the coverage probability of a confidence interval estimate of the population proportion $$p$$?

Accepted Answer

The actual proportion of confidence intervals that contain the true population proportion.

Question 13

Suppose you want to construct a 99% confidence interval for a population proportion. What is the critical value $$z_{\alpha/2}$$ you should use?

Accepted Answer

$$2.575$$

Question 14

A pollster wants to estimate the proportion of voters who support a new policy. She has no prior estimate for $$p$$ and wants the margin of error to be no more than $$0.04 at a 95$$% confidence level. What value should she use for $$\hat{p}$$ and $$\hat{q} in $$the sample size formula?

Accepted Answer

$$\hat{p} = 0.5$$, $$\hat{q} = 0.5$$

Question 15

Which of the following is a correct step in constructing a confidence interval for a population proportion $$p$$?

Accepted Answer

Find the critical value $$z_{\alpha/2}$$ corresponding to the desired confidence level.

Question 16

A survey of 950 students finds that 53% take online courses. The 95% confidence interval for the population proportion is $$0.498 \u003c p \u003c 0.562. $$Can we safely conclude that more than 50% of undergraduates take online courses?

Accepted Answer

No, because the confidence interval includes values below 0.50.

Question 17

Which confidence interval method involves adding 2 to the number of successes and 2 to the number of failures before calculating the interval?

Accepted Answer

Plus four confidence interval

Question 18

If a confidence interval for a population proportion is $$(0.58, 0.81)$$, what is the point estimate $$\hat{p}$$?

Accepted Answer

$$0.695$$

Question 19

Which of the following is a common misconception when interpreting a confidence interval?

Accepted Answer

There is a 95% chance that the true value of $$p$$ will fall between the interval limits.

Estimating Population Proportions and Determining Sample Sizes (Chapter 7 Study Notes)

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