Question 1

A Gallup poll surveyed 1487 adults and found that 43% have a Facebook page. What is the best point estimate for the proportion of all adults who have a Facebook page?

Accepted Answer

$$0.43$$

Question 2

Which of the following is the correct interpretation of a 95% confidence interval for a population proportion $$p$$ given by $$0.405 \u003c p \u003c 0.455$$?

Accepted Answer

We are 95% confident that the interval from $$0.405 to$$ $$0.455$$ actually does contain the true value of the population proportion $$p.$$

Question 3

Which formula is used to calculate the margin of error $$E$$ for estimating a population proportion?

Accepted Answer

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

Question 4

A researcher wants to estimate the proportion of adults who make online purchases with a margin of error of $$0.03 at a$$ $$95\%$$ confidence level. No prior estimate is available. What sample size should be used?

Accepted Answer

$$n = \left[ \dfrac{z_{\alpha/2}^2 \cdot 0.25}{E^2$} \right] = \left[ \dfrac{1.96^2$ \cdot 0.25}{0.03^2$} \right] = 1068$$

Question 5

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 6

Given a 95% confidence interval for a population mean $$\mu as$$ $$29.4 \u003c \mu \u003c 32.4$$, what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \dfrac{29.4 + 32.4}{2} = 30.9$$

Question 7

When estimating a population mean $$\mu$$ and the population standard deviation $$\sigma is $$unknown, which distribution should be used to construct the confidence interval?

Accepted Answer

Student $$t$$ distribution

Question 8

A sample of 15 birth weights has a mean of $$30.9 hg $$and $$\sigma = 2.9 hg. $$What is the margin of error $$E$$ for a 95% confidence interval?

Accepted Answer

$$E = 1.96 \cdot \dfrac{2.9}{\sqrt{15}} = 1.46760$$

Question 9

Which of the following statements about the Student $$t$$ distribution is FALSE?

Accepted Answer

The standard deviation of the Student $$t$$ distribution is always 1.

Question 10

A researcher wants to estimate the mean IQ score of statistics students with a margin of error of 3 points and 95% confidence. If $$\sigma = 15$$, what sample size is required?

Accepted Answer

$$n = \left[ \dfrac{z_{\alpha/2} \cdot \sigma}{E} \right]^2 = \left[ \dfrac{1.96 \cdot 15}{3} \right]^2 = 97$$

Question 11

Which of the following best describes a critical value $$z_{\alpha/2}$$?

Accepted Answer

A $$z$$ score that separates an area of $$\alpha/2 in $$the right tail of the standard normal distribution.

Question 12

If a 95% confidence interval for a population proportion $$p is$$ $$0.405 \u003c p \u003c 0.455$$, what is the margin of error $$E$$?

Accepted Answer

$$E = \dfrac{0.455 - 0.405}{2} = 0.025$$

Question 13

Which of the following is a correct formula for the confidence interval for a population mean $$\mu$$ when $$\sigma is $$known?

Accepted Answer

$$\bar{x} - z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}} \u003c \mu \u003c \bar{x} + z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}$$

Question 14

Which of the following is a requirement for using the Student $$t$$ distribution to construct a confidence interval for a mean?

Accepted Answer

The population is normally distributed or the sample size is greater than 30.

Question 15

A poll reports a 95% confidence interval for the proportion of voters supporting a candidate as $$0.52 \u003c p \u003c 0.60. $$What is the point estimate $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{0.52 + 0.60}{2} = 0.56$$

Question 16

Which of the following is TRUE regarding the effect of sample size on the reliability of poll results?

Accepted Answer

The reliability of poll results depends on the sample size, not the population size.

Estimating Parameters and Determining Sample Sizes: Confidence Intervals for Proportions and Means

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