Q: A manager samples 100 bottles and finds a sample mean of 12.79 ounces. The population standard deviation is 0.2 ounces. What is the 95% confidence interval for the population mean?

$$12.75 \text{ ounces to } 12.83 \text{ ounces}$$

Q: A business analyst wants to estimate the mean annual dining out expenditure for young professionals in Detroit. The sample mean is $$5,230, the population standard deviation is 500$$, and the sample size is 200. What is the 90% confidence interval for the mean?

$$5,171.84 \text{ to } 5,288.16$$

Q: A sample of 25 calls has a mean of 7.088 minutes and a sample standard deviation of 4.64 minutes. What is the 95% confidence interval for the mean call time using the t-distribution?

$$5.173 \text{ min to } 9.003 \text{ min}$$

Question 1

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

Accepted Answer

A single statistic calculated from a sample used to estimate a population parameter.

Question 2

A pollster reports that 82% of sampled adults favor banning texting while driving. What is this 82% called?

Accepted Answer

Point estimate

Question 3

Which formula is used to calculate the standard error of the sampling distribution for the mean when the population standard deviation is known?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$

Question 4

A manager samples 100 bottles and finds a sample mean of 12.79 ounces. The population standard deviation is 0.2 ounces. What is the 95% confidence interval for the population mean?

Accepted Answer

$$12.75 	ext{ ounces to } 12.83 	ext{ ounces}$$

Question 5

What happens to the margin of error if the confidence level is decreased, assuming all other factors remain constant?

Accepted Answer

The margin of error decreases.

Question 6

Which formula is used to calculate the margin of error for estimating the population mean when the population standard deviation is known?

Accepted Answer

$$e = z \frac{\sigma}{\sqrt{n}}$$

Question 7

A business analyst wants to estimate the mean annual dining out expenditure for young professionals in Detroit. The sample mean is $$5,230, the population standard deviation is 500$$, and the sample size is 200. What is the 90% confidence interval for the mean?

Accepted Answer

$$5,171.84 	ext{ to } 5,288.16$$

Question 8

Which statement correctly interprets a 90% confidence interval for a population mean?

Accepted Answer

90% of all possible confidence intervals constructed from samples of the same size will contain the population mean.

Question 9

If a manager increases the sample size from 100 to 400 bottles, what is the effect on the confidence interval for the mean fill amount?

Accepted Answer

The confidence interval becomes narrower.

Question 10

When the population standard deviation is unknown, which distribution is used to construct a confidence interval for the mean?

Accepted Answer

Student's t-distribution

Question 11

A sample of 25 calls has a mean of 7.088 minutes and a sample standard deviation of 4.64 minutes. What is the 95% confidence interval for the mean call time using the t-distribution?

Accepted Answer

$$5.173 	ext{ min to } 9.003 	ext{ min}$$

Question 12

Which formula is used to determine the required sample size for estimating a population mean when the population standard deviation is known?

Accepted Answer

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

Question 13

Which of the following is NOT a way to reduce the margin of error in a confidence interval estimate?

Accepted Answer

Increasing the confidence level

Question 14

What is the formula for the sample proportion?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Question 15

A marketing manager samples 100 customers and finds 62 used a voucher. What is the 95% confidence interval for the population proportion?

Accepted Answer

$$0.525 	ext{ to } 0.715$$

Question 16

Which formula is used to calculate the standard error for the sample proportion?

Accepted Answer

$$\sqrt{\frac{p(1-p)}{n}}$$

Question 17

Which formula is used to calculate the confidence interval estimate for a population proportion?

Accepted Answer

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

Question 18

Which condition must be met for the sampling distribution of the sample proportion to be approximately normal?

Accepted Answer

$$np \geq 5$$ 	ext{ and } $$n(1-p) \geq 5$$

Question 19

A regional manager wants a 90% confidence level and a margin of error of 0.50 gallon for estimating mean gasoline purchase. The estimated population standard deviation is 4.85. What sample size is required?

Accepted Answer

$$n = \left( \frac{1.645 	imes 4.85}{0.50} \$$right)^2$$ = 255$$

Estimating Single Population Parameters: Point Estimates, Confidence Intervals, and Sample Size

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