Question 1

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

Accepted Answer

A value calculated from a sample that is used to estimate a population parameter.

Question 2

Suppose a researcher wants to estimate the mean age of people in a city. Which of the following is the best example of a point estimator?

Accepted Answer

The sample mean age calculated from a random sample of residents.

Question 3

A confidence interval for the mean $$\mu is $$constructed using the formula $$\bar{x} \pm z \frac{\sigma}{\sqrt{n}}. $$What does the term $$z$$ represent in this formula?

Accepted Answer

The critical value from the standard normal distribution corresponding to the desired confidence level.

Question 4

If a 95% confidence interval for the mean diameter of logs is calculated as $$12.09 \pm 0.94$$, what does the value 0.94 represent?

Accepted Answer

The margin of error.

Question 5

Which of the following actions will decrease the width of a confidence interval for a population mean, assuming all other factors remain constant?

Accepted Answer

Increasing the sample size.

Question 6

A manager wants to estimate the mean diameter of logs within 0.50 inches at a 90% confidence level. The population standard deviation is 4.8 inches. What is the minimum sample size required? (Use $$z = 1.645$$ for 90% confidence.)

Accepted Answer

The minimum sample size is $$n = \left( \frac{z \sigma}{E} \$$right)^2$$ = \left( \frac{1.645 	imes 4.8}{0.5} \$$right)^2$$ = 249.6 \approx 250$$

Question 7

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 true population mean.

Question 8

If the sample size is increased from 30 to 100, what is the effect on the margin of error for a confidence interval, assuming all other factors remain constant?

Accepted Answer

The margin of error decreases.

Question 9

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

Accepted Answer

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

Question 10

A statistic is called unbiased if:

Accepted Answer

Its value in repeated samples is equal to the true value of the parameter.

Question 11

Suppose you are constructing a 99% confidence interval for a population mean. Compared to a 95% confidence interval, the 99% interval will:

Accepted Answer

Be wider.

Question 12

Which of the following is NOT an assumption for constructing a confidence interval for the mean when the population standard deviation is known?

Accepted Answer

The sample is not randomly selected.

Question 13

A researcher calculates a 90% confidence interval for the mean height of a plant species as $$15.2 \pm 2.1 cm. $$What is the interpretation of this interval?

Accepted Answer

We are 90% confident that the true mean height of the plant species is between 13.1 cm and 17.3 cm.

Question 14

If the population standard deviation $$\sigma is $$unknown, which of the following should be used to construct a confidence interval for the mean?

Accepted Answer

The sample standard deviation $$s$$ and the $$t-$$distribution.

Question 15

Which of the following best describes the effect of increasing the confidence level from 90% to 99%?

Accepted Answer

The confidence interval becomes wider.

Question 16

A sample of 100 cans from a population with $$\sigma = 0.20$$ produced a sample mean equal to 12.09. What is the 95% confidence interval for the population mean? (Use $$z = 1.96)$$

Accepted Answer

$$12.09 \pm 1.96 	imes \frac{0.20}{\sqrt{100}} = 12.09 \pm 0.0392$$

Question 17

Which of the following is a plausible reason for using a sample rather than a census to estimate a population parameter?

Accepted Answer

A census is often impractical, expensive, or impossible for large populations.

Question 18

Which of the following is the correct formula for a 95% confidence interval for the mean when the population standard deviation is known?

Accepted Answer

$$\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$$

Question 19

A confidence interval is said to be random because:

Accepted Answer

The interval varies from sample to sample, even though the center is fixed.

Estimation and Confidence Intervals in Statistics

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