Q: A poll of 1520 adults found that 52% never read newspapers in print. What is the margin of error (ME) for a 90% confidence interval for this proportion? Use $$z^* = 1.645.$$

$$ME = 1.645 \times \sqrt{\frac{0.52 \times 0.48}{1520}} \approx 0.0211$$

Q: A random sample of 1015 adults found that 45% believe the death penalty is applied unfairly. What is the margin of error for a 90% confidence interval? Use $$z^* = 1.645.$$

$$ME = 1.645 \times \sqrt{\frac{0.45 \times 0.55}{1015}} \approx 0.0255$$

Q: Given a sample proportion $$\hat{p} = 0.49$$ from $$n = 1015$$ adults, what is the standard error for the proportion?

$$SE = \sqrt{\frac{0.49 \times 0.51}{1015}} \approx 0.0157$$

Q: Which formula correctly represents the margin of error for a confidence interval for a proportion?

$$ME = z^* \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 1

Which of the following best describes the trade-off between certainty and precision in confidence intervals for proportions?

Accepted Answer

Increasing certainty requires a wider interval, which decreases precision.

Question 2

A poll of 1520 adults found that 52% never read newspapers in print. What is the margin of error (ME) for a 90% confidence interval for this proportion? Use $$z^* = 1.645.$$

Accepted Answer

$$ME = 1.645 	imes \sqrt{\frac{0.52 	imes 0.48}{1520}} \approx 0.0211$$

Question 3

If you want to decrease the margin of error for a 95% confidence interval without reducing your confidence level, which of the following should you do?

Accepted Answer

Increase the sample size.

Question 4

Which of the following statements is TRUE about a 99% confidence interval for a population proportion?

Accepted Answer

A 99% confidence interval is wider than a 95% confidence interval would be.

Question 5

A random sample of 1015 adults found that 45% believe the death penalty is applied unfairly. What is the margin of error for a 90% confidence interval? Use $$z^* = 1.645.$$

Accepted Answer

$$ME = 1.645 	imes \sqrt{\frac{0.45 	imes 0.55}{1015}} \approx 0.0255$$

Question 6

Which of the following is NOT a condition that must be checked before constructing a one-proportion z-interval?

Accepted Answer

Population mean is known

Question 7

Suppose you want to be more confident that your interval contains the true population proportion. What must you do to your confidence interval?

Accepted Answer

Make the interval wider.

Question 8

Given a sample proportion $$\hat{p} = 0.49$$ from $$n = 1015$$ adults, what is the standard error for the proportion?

Accepted Answer

$$SE = \sqrt{\frac{0.49 	imes 0.51}{1015}} \approx 0.0157$$

Question 9

A 95% confidence interval for the proportion of U.S. adults who think the death penalty is applied fairly is $$(0.459, 0.521). $$What does this mean?

Accepted Answer

We are 95% confident that the true proportion is between 0.459 and 0.521.

Question 10

If you do not have an estimate for $$\hat{p}$$, what value should you use to calculate the maximum margin of error for a proportion?

Accepted Answer

$$p = 0.5$$

Question 11

Which formula correctly represents the margin of error for a confidence interval for a proportion?

Accepted Answer

$$ME = z^* 	imes \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 12

A weather forecaster says, 'The high temperature will be between 40 below zero and 200 above.' What statistical concept does this best illustrate?

Accepted Answer

A confidence interval with high certainty but low precision.

Question 13

If you want to construct a 99% confidence interval instead of a 95% confidence interval, what will happen to the margin of error?

Accepted Answer

The margin of error will increase.

Question 14

Which of the following is a correct interpretation of a 95% confidence interval for a population proportion?

Accepted Answer

If we took many samples, about 95% of the intervals would contain the true population proportion.

Question 15

A poll of 1520 adults is used to estimate a population proportion. Which condition ensures that the sample is not too large relative to the population?

Accepted Answer

10% condition

Sampling Distribution Models and Confidence Intervals for Proportions

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