Question 1

Which of the following best describes a point estimate in the context of estimating a population proportion?

Accepted Answer

A single value used to estimate a population parameter.

Question 2

Suppose a survey of 362 drive-thru orders at McDonald's found that 33 were inaccurate. What is the sample proportion $$\hat{p} of $$inaccurate orders?

Accepted Answer

$$\hat{p} = \dfrac{33}{362} = 0.0912$$

Question 3

What does a 95% confidence interval for a population proportion mean?

Accepted Answer

95% of all possible confidence intervals constructed from repeated samples will contain the true population proportion.

Question 4

Given a sample proportion $$\hat{p}$$, sample size $$n$$, and critical value $$z_{\alpha/2}$$, which formula is used to calculate the margin of error $$E$$ for a confidence interval for a population proportion?

Accepted Answer

$$E = z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

Question 5

If a 95% confidence interval for a population proportion is $$0.0615 \u003c p \u003c 0.121$$, what is the margin of error $$E$$?

Accepted Answer

$$E = \dfrac{0.121 - 0.0615}{2} = 0.02975$$

Question 6

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

Accepted Answer

The sample must be a voluntary response sample.

Question 7

A poll reports that 70% of 1002 surveyed people said they voted, but official records show only 61% of eligible people voted. The 95% confidence interval for the proportion who said they voted is $$0.666 \u003c p \u003c 0.734. $$What can you conclude?

Accepted Answer

More people said they voted than actually did, since 61% is not in the confidence interval.

Question 8

Which formula should be used to determine the minimum sample size $$n$$ needed to estimate a population proportion $$p$$ with a specified margin of error $$E$$ and confidence level, when $$\hat{p} is $$unknown?

Accepted Answer

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

Question 9

What is the critical value $$z_{\alpha/2}$$ for a 99% confidence level?

Accepted Answer

$$z_{\alpha/2} = 2.575$$

Question 10

A bag of M&Ms is found to have a 95% confidence interval for the proportion of green M&Ms as $$0.131 to$$ $$0.267. $$What is the point estimate for the proportion of green M&Ms?

Accepted Answer

$$\hat{p} = \dfrac{0.267 + 0.131}{2} = 0.199$$

Question 11

Which of the following statements about confidence intervals is correct?

Accepted Answer

A confidence interval provides a range of values that may contain the true population proportion.

Question 12

If you want to estimate the proportion of California residents that are left-handed with a margin of error of 3% and a 99% confidence level, what is the minimum sample size required if you have no prior estimate for $$p$$?

Accepted Answer

$$n = \dfrac{(2.575)^2$ \cdot 0.25}{(0.03)^2$} = 1,847$$

Question 13

Which of the following is a common mistake when interpreting a confidence interval for a population proportion?

Accepted Answer

Assuming there is a 95% chance the true proportion is in the interval for this sample.

Question 14

A researcher wants to estimate the proportion of defective items in a shipment. She wants the estimate to be within 0.05 of the true proportion with 95% confidence. If she has no prior estimate for $$p$$, what sample size should she use?

Accepted Answer

$$n = \dfrac{(1.96)^2$ \cdot 0.25}{(0.05)^2$} = 384$$

Question 15

Which of the following best describes a critical value in the context of confidence intervals?

Accepted Answer

A value that separates significant statistics from non-significant ones.

Question 16

If the margin of error is given as a percentage, what must you do before using it in the sample size formula?

Accepted Answer

Convert it to a decimal.

Question 17

Which of the following is NOT a factor that affects the reliability of a poll's results?

Accepted Answer

The population size.

Question 18

A coin is tossed 100 times and comes up heads 56 times. Construct a 90% confidence interval for the proportion of heads. Use $$z_{\alpha/2} = 1.645.$$

Accepted Answer

$$0.466 \u003c p \u003c 0.654$$

Estimating a Population Proportion and Confidence Intervals

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