Q: A pollster wants to estimate the proportion of voters who support a new policy. The sample size is 200, and 60% support the policy. What is the standard error for the sample proportion?

$$\sqrt{\dfrac{0.6 \times 0.4}{200}}$$

Question 1

Which of the following is required to construct a confidence interval for a population proportion $$p$$?

Accepted Answer

The sample must be obtained by simple random sampling or through a randomized experiment.

Question 2

A researcher wants to estimate the proportion of students at a university who own a car. Which condition must be checked before constructing a confidence interval for the population proportion?

Accepted Answer

The sample size is large enough so that $$np \geq 5$$ and $$n(1-p) \geq 5.$$

Question 3

Which of the following is NOT a requirement for constructing a confidence interval for a population mean $$\mu$$ when the population standard deviation $$\sigma is $$unknown?

Accepted Answer

The population proportion must be known.

Question 4

A medical researcher collects a simple random sample of 100 patients to estimate the mean recovery time after a new treatment. The population standard deviation is unknown. Which confidence interval procedure should be used?

Accepted Answer

Use a $$t-$$interval for the population mean.

Question 5

Which formula is used to construct a confidence interval for a population proportion $$p$$?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$$

Question 6

A sample of 40 batteries is tested to estimate the mean lifetime. The population standard deviation is known. Which confidence interval should be used?

Accepted Answer

A $$z-$$interval for the population mean.

Question 7

Which of the following scenarios requires the use of a $$t-$$distribution rather than a $$z-$$distribution when constructing a confidence interval?

Accepted Answer

The population standard deviation $$\sigma is $$unknown and the sample size is small.

Question 8

A pollster wants to estimate the proportion of voters who support a new policy. The sample size is 200, and 60% support the policy. What is the standard error for the sample proportion?

Accepted Answer

$$\sqrt{\dfrac{0.6 	imes 0.4}{200}}$$

Question 9

Which of the following is a reason why a confidence interval for a population proportion $$p$$ may not be valid?

Accepted Answer

The sample was not obtained by simple random sampling.

Question 10

A researcher wants to estimate the mean height of adult males in a city. The sample size is 25, and the population standard deviation is unknown. The sample is approximately normal. Which confidence interval should be used?

Accepted Answer

A $$t-$$interval for the population mean.

Question 11

If a sample is not obtained by simple random sampling, what is the most likely consequence when constructing a confidence interval?

Accepted Answer

The confidence interval may not accurately reflect the population parameter.

Question 12

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we were to take many samples and construct a confidence interval from each, about 95% of those intervals would contain the true population mean.

Question 13

A sample of 50 patients is used to estimate the proportion who respond to a new drug. The sample proportion is 0.3. Which formula gives the margin of error for a 95% confidence interval?

Accepted Answer

$$1.96 	imes \sqrt{\dfrac{0.3 	imes 0.7}{50}}$$

Question 14

Which of the following statements is true regarding the use of the $$z-$$distribution for confidence intervals?

Accepted Answer

The $$z-$$distribution is used when the population standard deviation is known and the sample size is large.

Question 15

A company wants to estimate the average time it takes to assemble a product. The sample size is 10, the sample mean is 45 minutes, and the sample standard deviation is 5 minutes. The population is approximately normal. Which confidence interval should be used?

Accepted Answer

A $$t-$$interval for the population mean.

Question 16

Which of the following is a necessary condition for constructing a confidence interval for a population mean when the sample size is less than 30?

Accepted Answer

The population distribution must be approximately normal.

Section 9.3: Determining the Appropriate Confidence Interval Procedure

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