Q: A sample of 16 Toyota Camry owners reports a mean miles per gallon of 28.1 with a standard deviation of 2.38. What is the 95% confidence interval for the mean, given $$t_{0.025,15} = 2.131$$?

$$ 28.1 \pm 2.131 \times \frac{2.38}{\sqrt{16}} $$

Question 1

Which of the following best describes a point estimate for a population proportion?

Accepted Answer

The value of a statistic that estimates the value of a parameter.

Question 2

A poll surveyed 1,015 Americans, and 458 said they believe their federal income tax is too high. What is the point estimate for the proportion of Americans who believe this?

Accepted Answer

$$ \frac{458}{1015} = 0.451 $$

Question 3

Which statement correctly interprets a 95% confidence interval for a population proportion?

Accepted Answer

95% of all possible samples will result in confidence intervals that include the parameter.

Question 4

What is the formula for the margin of error $$E in a $$confidence interval for a population proportion?

Accepted Answer

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

Question 5

If you increase the level of confidence from 95% to 99%, what happens to the margin of error in a confidence interval for a population proportion?

Accepted Answer

The margin of error increases.

Question 6

Which formula is used to determine the sample size needed to estimate a population proportion $$p$$ with a specified margin of error $$E$$ and prior estimate $$\hat{p}$$?

Accepted Answer

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

Question 7

Which property distinguishes the Student’s t-distribution from the standard normal distribution?

Accepted Answer

The t-distribution is centered at 0 and has longer tails than the standard normal distribution.

Question 8

A sample of 16 Toyota Camry owners reports a mean miles per gallon of 28.1 with a standard deviation of 2.38. What is the 95% confidence interval for the mean, given $$t_{0.025,15} = 2.131$$?

Accepted Answer

$$ 28.1 \pm 2.131 	imes \frac{2.38}{\sqrt{16}} $$

Question 9

When is it appropriate to use the t-distribution to construct a confidence interval for a population mean?

Accepted Answer

When the sample size is large or the data are approximately normal with no outliers.

Question 10

Which formula gives the sample size required to estimate the population mean $$\mu$$ with margin of error $$E$$ and known standard deviation $$s$$?

Accepted Answer

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

Question 11

Which distribution is used to construct a confidence interval for the population variance and standard deviation?

Accepted Answer

Chi-square distribution

Question 12

What is the formula for a $$ (1-\alpha) 	imes 100\% $$ confidence interval for the population variance $$ \$$sigma^2$$ $$?

Accepted Answer

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

Question 13

Which of the following is NOT a requirement for using the bootstrap method to estimate a parameter?

Accepted Answer

The original sample must be drawn from a normal population.

Question 14

In bootstrapping, what is the purpose of resampling with replacement from the original sample?

Accepted Answer

To create many samples that mimic the variability of the population.

Question 15

A researcher wants to estimate the proportion of students who use public transportation. If no prior estimate is available, which value should be used for $$ \hat{p}  to $$maximize the required sample size?

Accepted Answer

$$ \hat{p} = 0.5 $$

Question 16

Which of the following statements about the chi-square distribution is TRUE?

Accepted Answer

It is not symmetric and its shape depends on the degrees of freedom.

Question 17

A 90% confidence interval for the standard deviation of car prices is ($$1955, 4055). $$What does this mean?

Accepted Answer

We are 90% confident that the population standard deviation of car prices is between $$1955 and 4055.$$

Question 18

Which method should be used to construct a confidence interval for the mean when the sample size is small and the data are not normal?

Accepted Answer

Nonparametric procedures or bootstrapping

Estimating Parameters and Constructing Confidence Intervals in Statistics

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