Question 1

Which of the following statements best describes the sampling distribution of the sample mean?

Accepted Answer

It is the distribution of all possible sample means from samples of the same size $$n$$ taken from the same population.

Question 2

Suppose you roll a fair die 5 times and record the proportion of odd numbers. If you repeat this process indefinitely, what can you say about the mean of all sample proportions?

Accepted Answer

It will be equal to the population proportion.

Question 3

Which of the following statistics is NOT an unbiased estimator of its corresponding population parameter?

Accepted Answer

Sample standard deviation $$s$$

Question 4

A researcher collects 100 samples of size $$n=30$$ from a population and calculates the sample means. What shape will the distribution of these sample means most likely have?

Accepted Answer

Normal distribution

Question 5

Which formula correctly represents the sample proportion $$\hat{p}$$?

Accepted Answer

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

Question 6

Why is the sample standard deviation $$s$$ considered a biased estimator of the population standard deviation $$\sigma$$?

Accepted Answer

Because the mean of the sampling distribution of $$s$$ does not equal $$\sigma.$$

Question 7

In the context of sampling distributions, what does it mean for a statistic to 'target' a population parameter?

Accepted Answer

The mean of the sampling distribution of the statistic equals the population parameter.

Question 8

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

Accepted Answer

It tends to be skewed to the right.

Question 9

A hospital administrator wants to estimate the proportion of patients who recover within 3 days after surgery. She takes several random samples of size $$n=50$$ and calculates the sample proportions. What property of the sampling distribution of $$\hat{p}$$ allows her to use these sample proportions to estimate the population proportion?

Accepted Answer

The mean of the sample proportions equals the population proportion.

Question 10

Which of the following is a correct definition of an unbiased estimator?

Accepted Answer

A statistic whose sampling distribution has a mean equal to the population parameter.

Question 11

If you repeatedly roll a die 5 times and calculate the mean of the results, what is the expected value of the sample mean as the number of trials approaches infinity?

Accepted Answer

It will approach the population mean $$\mu = 3.5.$$

Question 12

Which of the following is a biased estimator?

Accepted Answer

Sample range

Question 13

A statistician is interested in the distribution of all possible sample variances from samples of size $$n=10$$ drawn from a population. What is this distribution called?

Accepted Answer

Sampling distribution of the sample variance

Question 14

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

Accepted Answer

Its variance equals the population variance.

Question 15

A pharmaceutical company wants to estimate the average effect of a new drug. They take multiple samples of patients and calculate the sample means. What allows them to use the sample means to estimate the population mean?

Accepted Answer

The mean of the sample means equals the population mean.

Question 16

Which of the following is true about the distribution of sample proportions $$\hat{p}$$ when the sample size is sufficiently large?

Accepted Answer

It tends to be approximately normal.

Question 17

Which of the following is a correct formula for the population proportion $$p$$?

Accepted Answer

$$p = \frac{x}{N}$$

Question 18

Which of the following statistics is most likely to have a sampling distribution that is NOT symmetric?

Accepted Answer

Sample variance $$s^2$$

Question 19

A sample statistic is used to estimate a population parameter. What is this sample statistic called?

Accepted Answer

Estimator

Question 20

Which of the following is NOT a biased estimator?

Accepted Answer

Sample variance $$s^2$$

Sampling Distributions and Estimators: Essentials of Statistics Chapter 6 Study Notes

Study Guide - Practice Questions

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