Q: A survey of 1003 U.S. adults found that 451 believe it is important to share American customs and traditions. What is the 95% confidence interval for the population proportion?

$$0.45 \pm 1.96 \sqrt{\frac{0.45 \times 0.55}{1003}}$$

Question 1

A random sample of 36 top-rated roller coasters has an average height of 165 feet and a standard deviation of 67 feet. Construct a 90% confidence interval for the mean height. Which formula should you use?

Accepted Answer

Use $$\bar{x} \pm t_{\alpha/2} \frac{s}{\sqrt{n}}$$

Question 2

You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. No preliminary estimate is available. What value should you use for $$\hat{p}$$ when calculating the minimum sample size?

Accepted Answer

$$\hat{p} = 0.5$$

Question 3

A survey of 2202 U.S. adults found that 1167 think antibiotics are effective against viral infections. What is the point estimate for the population proportion?

Accepted Answer

$$\frac{1167}{2202} \approx 0.53$$

Question 4

Which of the following best describes the margin of error for a confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$E = t_{\alpha/2} \frac{s}{\sqrt{n}}$$

Question 5

A 95% confidence interval for a population mean is calculated as $$(12.5, 24.0). $$What is the sample mean?

Accepted Answer

$$\bar{x} = 18.25$$

Question 6

In a survey of 2223 U.S. adults, 1334 say an occupation as an athlete is prestigious. Construct a 90% confidence interval for the population proportion. Which formula should you use?

Accepted Answer

$$\hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 7

If you want your estimate of a population proportion to be accurate within 5% with 95% confidence, and a prior study found $$\hat{p} = 0.33$$, what is the minimum sample size required?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2}}{E} \$$right)^2$$ \hat{p}(1-\hat{p})$$

Question 8

A sample of 10 people who start work at 8:00 a.m. has waking times (in minutes past 5:00 a.m.) as follows: 18, 24, 15, 12, 16, 20, 22, 15, 18, 19. What is the sample mean waking time?

Accepted Answer

$$17.9$$ minutes

Question 9

Which of the following statements is true about the width of a confidence interval for a population proportion?

Accepted Answer

The width decreases as the sample size increases.

Question 10

You are constructing a 99% confidence interval for a population mean with a sample size of 15. Which critical value should you use?

Accepted Answer

$$t_{0.005, 14}$$

Question 11

A survey of 1003 U.S. adults found that 451 believe it is important to share American customs and traditions. What is the 95% confidence interval for the population proportion?

Accepted Answer

$$0.45 \pm 1.96 \sqrt{\frac{0.45 	imes 0.55}{1003}}$$

Question 12

If the population standard deviation is known, which distribution should you use to construct a confidence interval for the mean?

Accepted Answer

Standard normal ($$z) $$distribution

Question 13

A 90% confidence interval for a population mean is $$(25.6, 36.8). $$What is the margin of error?

Accepted Answer

$$5.6$$

Question 14

Which of the following is NOT a requirement for constructing a confidence interval for a population mean using the $$t-$$distribution?

Accepted Answer

The population standard deviation must be known.

Question 15

In a survey, 745 out of 1035 adults say they want the U.S. to play a leading role in global affairs. What is the sample proportion?

Accepted Answer

$$\frac{745}{1035} \approx 0.72$$

Question 16

If you increase the confidence level from 90% to 99% while keeping the sample size the same, what happens to the margin of error?

Accepted Answer

The margin of error increases.

Statistics Review: Confidence Intervals, Sample Size, and Proportions

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