Q: A poll found that 60% of voters support a new law, based on a sample of 400 voters. What is the standard error for the sample proportion?

$$ \sqrt{\frac{0.6 \times 0.4}{400}} $$

Q: A hospital administrator wants to estimate the average wait time in the emergency room. She wants to be 99% confident that the estimate is within 2 minutes of the true mean. The population standard deviation is estimated to be 8 minutes. What is the minimum sample size required?

$$ n = \left( \frac{2.576 \times 8}{2} \$$right)^2$$ = 106.0 $$

Q: A sample of 100 patients found that 30% had a certain medical condition. Construct a 90% confidence interval for the population proportion. (Use $$ z^* = 1.645 )$$

$$ 0.3 \pm 1.645 \times \sqrt{\frac{0.3 \times 0.7}{100}} $$

Question 1

Which of the following best describes a 'target parameter' in statistics?

Accepted Answer

A numerical summary of a population that we wish to estimate using sample data.

Question 2

A researcher wants to estimate the average height of adult males in a city. Which of the following is the most appropriate target parameter?

Accepted Answer

The mean height of all adult males in the city.

Question 3

Which formula is used to construct a confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

$$ \bar{x} \pm z^* \frac{\sigma}{\sqrt{n}} $$

Question 4

A 95% confidence interval for a population mean is calculated as $$ (50, 60) . $$What does this mean?

Accepted Answer

We are 95% confident that the interval from 50 to 60 contains the population mean.

Question 5

Which of the following is the correct formula for a confidence interval for a population proportion?

Accepted Answer

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

Question 6

A poll found that 60% of voters support a new law, based on a sample of 400 voters. What is the standard error for the sample proportion?

Accepted Answer

$$ \sqrt{\frac{0.6 	imes 0.4}{400}} $$

Question 7

Which condition must be met to use the large sample confidence interval for a population proportion?

Accepted Answer

$$ n\hat{p} \geq 10 $$ and $$ n(1-\hat{p}) \geq 10 $$

Question 8

A company wants to estimate the proportion of defective products with a margin of error no greater than 0.03 at a 95% confidence level. If no prior estimate is available, what value should be used for $$ \hat{p}  in $$the sample size formula?

Accepted Answer

$$ 0.5 $$

Question 9

Which formula is used to determine the minimum sample size needed to estimate a population mean with a specified margin of error $$ E $$ and confidence level?

Accepted Answer

$$ n = \left( \frac{z^* \sigma}{E} \$$right)^2$$ $$

Question 10

A hospital administrator wants to estimate the average wait time in the emergency room. She wants to be 99% confident that the estimate is within 2 minutes of the true mean. The population standard deviation is estimated to be 8 minutes. What is the minimum sample size required?

Accepted Answer

$$ n = \left( \frac{2.576 	imes 8}{2} \$$right)^2$$ = 106.0 $$

Question 11

A sample of 100 patients found that 30% had a certain medical condition. Construct a 90% confidence interval for the population proportion. (Use $$ z^* = 1.645 )$$

Accepted Answer

$$ 0.3 \pm 1.645 	imes \sqrt{\frac{0.3 	imes 0.7}{100}} $$

Question 12

If a 95% confidence interval for a population mean is $$ (12, 18) $$, what is the margin of error?

Accepted Answer

$$ 3 $$

Question 13

Which of the following would increase the width of a confidence interval for a population mean?

Accepted Answer

Increasing the confidence level from 95% to 99%.

Question 14

A researcher wants to estimate the proportion of people who prefer a new product. She wants a margin of error of 0.04 at a 95% confidence level. What is the minimum sample size required if $$ \hat{p} = 0.6 $$? (Use $$ z^* = 1.96 )$$

Accepted Answer

$$ n = \frac{(1.96)^2$ 	imes 0.6 	imes 0.4}{(0.04)^2$} = 576 $$

Question 15

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A 99% confidence interval is wider than a 90% confidence interval for the same data.

Chapter 7: Confidence Intervals and Estimation in Statistics

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