Question 1

Which of the following best describes the Central Limit Theorem?

Accepted Answer

It states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 2

A manufacturer wants to estimate the mean weight of its product. Which formula should be used to calculate the standard error of the sample mean?

Accepted Answer

$$\frac{\sigma}{\sqrt{n}}$$

Question 3

When can the sampling distribution of the sample proportion be approximated by a normal distribution?

Accepted Answer

When $$np \geq 10$$ and $$n(1-p) \geq 10$$

Question 4

A researcher wants to construct a 95% confidence interval for the mean income of a city. Which of the following is NOT required?

Accepted Answer

The population mean

Question 5

Which factor does NOT influence the margin of error in a confidence interval for the mean?

Accepted Answer

Population mean

Question 6

A company wants to estimate the proportion of defective items in a shipment. Which formula should be used to calculate the standard error of the sample proportion?

Accepted Answer

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

Question 7

If a sample size increases, what happens to the margin of error for a confidence interval?

Accepted Answer

It decreases

Question 8

A medical researcher compares the mean blood pressure before and after treatment in the same group of patients. Which confidence interval should be used?

Accepted Answer

Confidence interval for the difference between paired means

Question 9

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

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 10

A business analyst wants to determine the sample size needed to estimate a population proportion with a margin of error of 0.03 at 95% confidence. Which formula should be used?

Accepted Answer

$$n = \frac{z^2$ p(1-p)}{E^2$}$$

Question 11

Which statement is TRUE about confidence intervals for the difference between two means from independent samples?

Accepted Answer

The confidence interval estimates the difference in population means.

Question 12

A survey of 1000 voters finds that 520 support a new policy. What is the sample proportion?

Accepted Answer

$$0.52$$

Question 13

Which of the following is NOT a step in constructing a confidence interval for the population mean?

Accepted Answer

Calculate the population mean

Question 14

A pharmaceutical company wants to compare the mean recovery times for two drugs using independent samples. Which formula should be used for the standard error of the difference between means?

Accepted Answer

$$\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 15

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

Accepted Answer

If we repeated the sampling process many times, about 95% of the intervals would contain the population mean.

Exam Review: Sampling Distributions and Confidence Interval Estimation

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