Question 1

Which of the following best describes the difference between a statistic and a parameter?

Accepted Answer

A statistic is a descriptive measure for a sample, while a parameter is for a population.

Question 2

Given a population of 5 values: 2, 4, 6, 8, 10, what is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{2+4+6+8+10}{5} = 6$$

Question 3

Which symbol is used to represent the population standard deviation?

Accepted Answer

$$\sigma$$

Question 4

What is the formula for the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x - \mu)^2$}{N}$$

Question 5

Why do we use $$n-1$$ instead of $$n in $$the formula for sample variance?

Accepted Answer

To make the sample variance as close as possible to the population variance.

Question 6

If a population has values 3, 7, 7, 9, what is the population standard deviation $$\sigma$$? (Round to two decimal places)

Accepted Answer

$$\sigma = \sqrt{\frac{(3-6.5)^2$ + (7-6.5)^2$ + (7-6.5)^2$ + (9-6.5)^2$}{4}} = \sqrt{5.25} \approx 2.29$$

Question 7

Which of the following is NOT a descriptive measure for a population?

Accepted Answer

Sample mean ($$x\bar{})$$

Question 8

A researcher collects data from all patients in a hospital for a week. Which term best describes the mean calculated from this data?

Accepted Answer

Population mean ($$\mu)$$

Question 9

If the population mean $$\mu is 12 $$and the population size $$N is 4$$, which formula would you use to compute the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x - 12)^2$}{4}$$

Question 10

Which of the following statements is TRUE regarding the formulas for variance and standard deviation?

Accepted Answer

Sample variance divides by $$n-1$$, population variance divides by $$N.$$

Question 11

A population consists of the numbers 1, 2, 3, 4, 5. What is the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{(1-3)^2$ + (2-3)^2$ + (3-3)^2$ + (4-3)^2$ + (5-3)^2$}{5} = \frac{10}{5} = 2$$

Question 12

Which of the following is a parameter?

Accepted Answer

Population mean ($$\mu)$$

Question 13

A pharmaceutical company wants to know the average effectiveness of a new drug for all patients worldwide. Which measure are they trying to estimate?

Accepted Answer

Population mean ($$\mu)$$

Question 14

If you have a sample of 10 students' test scores, which symbol would you use for the sample size?

Accepted Answer

$$n$$

Question 15

Which formula would you use to calculate the population standard deviation $$\sigma$$ after finding the mean $$\mu$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x - \mu)^2$}{N}}$$

Question 16

A population has values 5, 7, 9. What is the computing formula for the population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum x^2$}{N} - \mu^2$

Question 17

Which of the following is a reason why the formulas for sample variance and population variance are different?

Accepted Answer

Sample variance uses $$n-1 to $$better estimate the population variance.

Question 18

If a population has values 2, 4, 6, 8, what is the population mean $$\mu$$ and population standard deviation $$\sigma$$?

Accepted Answer

$$\mu = 5$$, $$\sigma = \sqrt{5}$$

Descriptive Measures for Populations in Statistics

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