Q: If the standard deviation of a data set is 5, what is the variance?

$$\text{Variance} = 5^2$ = 25$$

Q: A bag contains 4 red, 5 blue, and 6 green marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

$$\frac{5}{15} \times \frac{4}{14} = \frac{20}{210} = \frac{2}{21}$$

Question 1

Which of the following is an example of data measured at the interval level?

Accepted Answer

The temperature in Celsius recorded each hour during a day.

Question 2

A researcher wants to study the average commute time for employees at a large company. She divides the employees into departments and randomly selects a few departments, then surveys all employees in those departments. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following best describes continuous data?

Accepted Answer

The height of students measured in centimeters.

Question 4

Given the following frequency distribution for exam scores:

Class: 60-69, Frequency: 3
Class: 70-79, Frequency: 7
Class: 80-89, Frequency: 10
Class: 90-99, Frequency: 5

What is the class midpoint for the class 80-89?

Accepted Answer

$$\frac{80+89}{2} = 84.5$$

Question 5

A frequency histogram is constructed for a set of test scores. Which of the following is NOT a correct guideline for constructing the histogram?

Accepted Answer

Leave gaps between the bars to indicate separate classes.

Question 6

Given the following data: 4, 7, 9, 12, 15. What is the midrange?

Accepted Answer

$$\frac{4+15}{2} = 9.5$$

Question 7

A distribution of test scores is described as 'skewed right.' Which of the following statements is most likely true?

Accepted Answer

The mean is greater than the median.

Question 8

Given the following frequencies and midpoints for a frequency distribution:

Class Midpoints: 10, 20, 30
Frequencies: 2, 5, 3

Calculate the mean using the formula $$\bar{x} = \frac{\sum(f \cdot x)}{\sum f}.$$

Accepted Answer

$$\bar{x} = \frac{(2 \cdot 10) + (5 \cdot 20) + (3 \cdot 30)}{2+5+3} = \frac{20+100+90}{10} = \frac{210}{10} = 21$$

Question 9

A student scored 82 on a test where the mean was 75 and the standard deviation was 4. What is the student's z-score?

Accepted Answer

$$z = \frac{82 - 75}{4} = 1.75$$

Question 10

If the standard deviation of a data set is 5, what is the variance?

Accepted Answer

$$	ext{Variance} = 5^2$ = 25$$

Question 11

In a medical study, 20% of patients experience side effects from a drug. If 5 patients are selected at random, what is the probability that at least one experiences side effects?

Accepted Answer

$$1 - (0.8)^5$ = 1 - 0.32768 = 0.67232$$

Question 12

A bag contains 4 red, 5 blue, and 6 green marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

Accepted Answer

$$\frac{5}{15} 	imes \frac{4}{14} = \frac{20}{210} = \frac{2}{21}$$

Question 13

A student is randomly assigned a locker numbered from 1 to 100. What is the probability that the locker number is a multiple of 5 or 7?

Accepted Answer

$$\frac{20 + 14 - 2}{100} = \frac{32}{100} = 0.32$$

Question 14

A data value is considered significantly low if its z-score is:

Accepted Answer

$$z \u003c -2$$

Question 15

A teacher wants to select a sample of students from a list of 200 by choosing every 10th student. Which sampling method is this?

Accepted Answer

Systematic sampling

Question 16

Given the following data: 2, 4, 4, 6, 8, 10. What is the mode?

Accepted Answer

4

Question 17

A set of data has the following values: 5, 7, 9, 12, 15. What is the percentile rank of the value 12?

Accepted Answer

$$\frac{4}{5} 	imes 100 = 80\%$$

Question 18

A frequency distribution has classes: 10-19, 20-29, 30-39. What are the class boundaries for the class 20-29?

Accepted Answer

19.5 and 29.5

Question 19

A researcher wants to ensure that her sample represents all age groups in a population. She divides the population into age groups and randomly selects individuals from each group. Which sampling method is she using?

Accepted Answer

Stratified sampling

Introductory Statistics Exam 1 Study Guide

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