Question 1

Which of the following best describes a point estimate in statistics?

Accepted Answer

A single value used to approximate a population parameter.

Question 2

A Pew Research Center poll found that 70% of 1501 randomly selected adults believe in global warming. What is the best point estimate of the population proportion?

Accepted Answer

$$0.70$$

Question 3

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

Accepted Answer

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

Question 4

If you want to be 95% confident that your sample proportion is within 0.03 of the true population proportion, and you have no prior estimate for $$\hat{p}$$, what value should you use for $$\hat{p}\hat{q} in $$the sample size formula?

Accepted Answer

$$0.25$$

Question 5

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A 95% confidence interval means that if we repeated the sampling process many times, about 95% of the intervals would contain the population parameter.

Question 6

Given $$n = 40$$, $$\bar{x} = 172.55$$, and $$\sigma = 26$$, what is the 95% confidence interval for the population mean $$\mu$$? (Use $$z_{0.025} = 1.96)$$

Accepted Answer

$$164.49 \u003c \mu \u003c 180.61$$

Question 7

Which distribution should be used to construct a confidence interval for the population mean when the population standard deviation is unknown and the sample size is small?

Accepted Answer

Student t distribution

Question 8

A sample of 49 subjects has a mean change in cholesterol of $$0.4 mg/dL $$and a standard deviation of $$21.0 mg/dL. $$Using a 95% confidence level and $$t_{0.025,48} \approx 2.009$$, what is the margin of error?

Accepted Answer

$$6.027$$

Question 9

Which of the following is NOT a property of the chi-square distribution?

Accepted Answer

It can take negative values.

Question 10

Given a sample variance $$s^2$$ from a normally distributed population, which formula gives the confidence interval for the population variance $$\$$sigma^2$$ using the chi-square distribution?

Accepted Answer

$$\left( \frac{(n-1)s^2$}{\$$chi^2$$_{\alpha/2}}, \frac{(n-1)s^2$}{\$$chi^2$$_{1-\alpha/2}} \right)$$

Question 11

A researcher wants to estimate the mean IQ of statistics students with a margin of error of 3 IQ points and a population standard deviation of 15. What sample size is needed for 95% confidence? ($$z_{0.025} = 1.96)$$

Accepted Answer

$$n = 97$$

Question 12

Which of the following is the correct formula for the sample size needed to estimate a population mean with known standard deviation $$\sigma$$ and margin of error $$E$$?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2} \sigma}{E} \$$right)^2$$

Question 13

A 95% confidence interval for the mean change in LDL cholesterol after garlic treatment is $$-5.6 \u003c \mu \u003c 6.4. $$What does this interval suggest?

Accepted Answer

There is no significant evidence that garlic treatment affects LDL cholesterol.

Question 14

Which of the following is the best point estimate of the population variance $$\$$sigma^2$$?

Accepted Answer

The sample variance $$s^2$$

Question 15

If a confidence interval for a population proportion $$p is$$ $$(0.677, 0.723)$$, what is the margin of error?

Accepted Answer

$$0.023$$

Estimates and Sample Sizes: Confidence Intervals and Sample Size Determination

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