Question 1

Which of the following best describes a population parameter?

Accepted Answer

A numerical descriptive measure of a population, usually unknown.

Question 2

Suppose you are studying the average sleep time of all university students. You collect data from a random sample of 50 students. What is the sample mean an example of?

Accepted Answer

A sample statistic

Question 3

Which formula correctly gives the standard error of the mean for a sample of size $$n$$ from a population with standard deviation $$\sigma$$?

Accepted Answer

$$\sigma / \sqrt{n}$$

Question 4

A researcher wants to estimate the proportion of defective steel sheets produced in a factory. Which symbol represents the population proportion and which represents the sample proportion?

Accepted Answer

Population: $$p$$, Sample: $$\hat{p}$$

Question 5

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

For large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population's distribution.

Question 6

If the mean of the sampling distribution of a statistic equals the parameter it estimates, the statistic is:

Accepted Answer

An unbiased estimator

Question 7

A company wants to estimate the average thickness of steel sheets. They take 25 random measurements. According to the Central Limit Theorem, what is the shape of the sampling distribution of the sample mean?

Accepted Answer

It will be approximately normal.

Question 8

Which of the following is NOT a property of the sampling distribution of the sample mean $$\bar{x}$$?

Accepted Answer

It is always normal, regardless of sample size.

Question 9

A medical researcher collects blood pressure readings from a sample of 100 patients. The population standard deviation is known to be 12 mmHg. What is the standard error of the mean?

Accepted Answer

$$12 / \sqrt{100}$$

Question 10

Which of the following scenarios best illustrates the concept of a sampling distribution?

Accepted Answer

Plotting the means of many samples of the same size from a population.

Question 11

If a sample statistic consistently overestimates the population parameter, it is considered:

Accepted Answer

Biased

Question 12

A factory manager wants to estimate the variance in the thickness of steel sheets. Which symbols represent the population variance and the sample variance?

Accepted Answer

Population: $$\$$sigma^2$$, Sample: s^2$

Question 13

Which of the following is an example of a real-world application of the Central Limit Theorem?

Accepted Answer

Using the average of a large sample of daily temperatures to estimate the mean temperature for a city.

Question 14

A sample statistic is said to have minimum variance if:

Accepted Answer

Its sampling distribution has the smallest possible spread among all unbiased estimators.

Question 15

Which of the following formulas represents the expected value of an unbiased estimator $$\hat{	heta}$$ for a population parameter $$	heta$$?

Accepted Answer

$$E(\hat{	heta}) = 	heta$$

Question 16

A researcher flips two coins and records the number of heads. What is the probability of getting exactly one head?

Accepted Answer

$$1/2$$

Question 17

Which of the following is true about the mean and standard deviation of the sampling distribution of the sample mean $$\bar{x}$$?

Accepted Answer

Mean is $$\mu$$, standard deviation is $$\sigma / \sqrt{n}.$$

Question 18

If a sample statistic has a sampling distribution with a mean not equal to the population parameter, it is:

Accepted Answer

A biased estimator

Question 19

A hospital administrator wants to estimate the average length of stay for patients. She takes a random sample of 64 patients. The population standard deviation is 8 days. What is the standard error of the mean?

Accepted Answer

$$8 / \sqrt{64}$$

Question 20

Which of the following best describes the purpose of a sampling distribution in inferential statistics?

Accepted Answer

To show how a sample statistic varies from sample to sample.

Sampling Distributions: Concepts, Properties, and Applications

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