Question 1

Which of the following best describes a sampling distribution?

Accepted Answer

The distribution of all possible values of a statistic when all possible samples of the same size are taken from a population.

Question 2

According to the Central Limit Theorem, what happens to the distribution of sample means as the sample size increases?

Accepted Answer

It becomes more normal, regardless of the population's distribution.

Question 3

If the population mean is $$\mu$$ and the population variance is $$\$$sigma^2$$, what is the expected value of the sample mean $$\overline{X}$$?

Accepted Answer

$$\mu$$

Question 4

Which of the following statements about the distribution of sample variances is correct?

Accepted Answer

It is skewed to the right and does not follow a normal distribution.

Question 5

A researcher takes many random samples of size $$n$$ from a population and calculates the sample proportion $$\hat{p}$$ for each. What is the distribution of these sample proportions called?

Accepted Answer

Sampling distribution of the sample proportion

Question 6

Which of the following is true about the mean of the sampling distribution of the sample variance $$s^2$$?

Accepted Answer

It equals the population variance $$\$$sigma^2$$.

Question 7

Suppose the population proportion is $$p = 0.4. If $$you take many samples of size $$n = 100$$, what is the expected mean of the sampling distribution of the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.4$$

Question 8

Which of the following best explains why the sample mean $$\overline{X} is an $$unbiased estimator of the population mean $$\mu$$?

Accepted Answer

The expected value of $$\overline{X}$$ equals $$\mu.$$

Question 9

A hospital administrator wants to estimate the average length of stay for patients. She takes 50 random samples of 30 patients each and calculates the mean for each sample. What is the distribution of these means called?

Accepted Answer

Sampling distribution of the sample mean

Question 10

If the population variance is $$\$$sigma^2$$ = 25$$ and the sample size is $$n = 100$$, what is the variance of the sampling distribution of the sample mean?

Accepted Answer

$$\frac{25}{100}$$

Question 11

Which of the following is NOT a property of the sampling distribution of the sample mean?

Accepted Answer

It is always skewed to the right.

Question 12

Why do methods for normal distributions not apply to the sampling distribution of sample variances?

Accepted Answer

Because the distribution of sample variances is skewed to the right.

Question 13

If a population is not normally distributed, what does the Central Limit Theorem say about the distribution of the sample mean for large $$n$$?

Accepted Answer

It will be approximately normal.

Question 14

A quality control manager samples 40 light bulbs from a factory and records the proportion that fail. If she repeats this process many times, what is the expected value of the sample proportions?

Accepted Answer

The population proportion of defective bulbs.

Question 15

Which formula gives the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

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

Sampling Distributions and the Central Limit Theorem: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards