Question 1

A Pew Research Center survey of 1007 adults found that 85% know what Twitter is. What is the best point estimate for the population proportion $$p$$?

Accepted Answer

$$0.85$$

Question 2

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 3

Suppose you want to estimate the proportion of adults who buy clothing online. You have no prior estimate for $$\hat{p}. $$What value should you use for $$\hat{p}$$ when determining the minimum sample size required?

Accepted Answer

$$0.5$$

Question 4

Given a 95% confidence interval for a population proportion $$p is$$ $$(0.278, 0.338)$$, what is the margin of error $$E$$?

Accepted Answer

$$E = \frac{0.338 - 0.278}{2} = 0.03$$

Question 5

A clinical trial using the XSORT method resulted in 574 babies, 525 of whom were girls. Construct a 95% confidence interval for the proportion of girls. Which formula should you use for the margin of error $$E$$?

Accepted Answer

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

Question 6

A manager wants to estimate the percentage of U.S. adults who use the internet. If a previous poll found 73% use the internet, what is the minimum sample size needed for a 99% confidence level and a margin of error of 0.03?

Accepted Answer

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

Question 7

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A confidence interval provides a range of plausible values for a population parameter.

Question 8

A sample of 49 subjects treated with garlic had a mean LDL cholesterol change of $$0.4 mg/dL $$and a standard deviation of $$21.0 mg/dL. $$Which distribution should be used to construct a 95% confidence interval for the mean change?

Accepted Answer

The $$t-$$distribution, because $$\sigma is $$unknown.

Question 9

Given a confidence interval for a mean is $$(98.0, 98.4)$$, what is the point estimate $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{98.0 + 98.4}{2} = 98.2$$

Question 10

A sample of 40 men has a mean weight of $$172.55 lb. If $$the population standard deviation is $$26 lb$$, what is the 95% confidence interval for the population mean weight? (Use $$z_{0.025} = 1.96)$$

Accepted Answer

$$172.55 \pm 1.96 \cdot \frac{26}{\sqrt{40}}$$

Question 11

You want to estimate the mean IQ of statistics students. The population standard deviation is known to be $$15. $$What is the minimum sample size needed for a 95% confidence level and a margin of error of $$3 IQ $$points? (Use $$z_{0.025} = 1.96)$$

Accepted Answer

$$n = \left( \frac{1.96 \cdot 15}{3} \$$right)^2$$

Question 12

A 99% confidence interval for the mean number of calories in a type of cookie is calculated from a sample of 15 cookies. The population standard deviation is unknown. Which interval should you use?

Accepted Answer

A $$t-$$interval

Question 13

A poll reports a 95% confidence interval for a proportion as $$(0.58, 0.81). $$What is the best point estimate for the population proportion?

Accepted Answer

$$\hat{p} = \frac{0.58 + 0.81}{2} = 0.695$$

Question 14

Which of the following is a common misconception about poll reliability?

Accepted Answer

Poll results are unreliable if the sample size is a small percentage of the population size.

Question 15

A sample of 106 healthy humans has a mean body temperature of $$98.2^\circF $$and a standard deviation of $$0.62^\circF. $$What is the 99% confidence interval for the mean body temperature? (Assume $$t_{0.005, 105} \approx 2.626)$$

Accepted Answer

$$98.2 \pm 2.626 \cdot \frac{0.62}{\sqrt{106}}$$

Question 16

You are designing a study to estimate the mean pulse rate of adult males. The pulse rates in a sample of 154 males range from 43 to 123 bpm. Using the range rule of thumb, what is the estimated standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \frac{123 - 43}{4} = 20$$

Question 17

A 98% confidence interval for the mean mercury content in tuna sushi is calculated from a sample. If the interval is $$(0.54, 1.25)$$ ppm, what can you conclude about the FDA guideline of 1 ppm?

Accepted Answer

There is evidence that the mean mercury content could exceed the FDA guideline.

Question 18

Which formula is used to calculate the margin of error $$E$$ for a confidence interval for a population mean when $$\sigma is $$known?

Accepted Answer

$$E = z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$$

Estimating Population Proportions and Means: Confidence Intervals and Sample Size Determination

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