Q: If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.4$$, and $$A$$ and $$B$$ are disjoint, what is $$P(A \text{ or } B)$$?

$$P(A \text{ or } B) = 0.3 + 0.4 = 0.7$$

Question 1

What is the main issue with the bar chart shown above?

Accepted Answer

The y-axis does not start at 0, which exaggerates the difference between the two years.

Question 2

Which of the following best describes the difference between a population and a sample?

Accepted Answer

A population includes all members of a group, while a sample includes only a subset of that group.

Question 3

Which of the following is an example of practical significance but NOT statistical significance?

Accepted Answer

A new medication reduces recovery time by 0.1 days, but the difference is not meaningful to patients.

Question 4

Which of the following is a pitfall of analyzing data?

Accepted Answer

Drawing misleading conclusions from voluntary response samples.

Question 5

Which of the following is a quantitative variable?

Accepted Answer

The number of books a student owns.

Question 6

A researcher divides a city into neighborhoods and randomly selects several neighborhoods. She then surveys every household in those selected neighborhoods. What sampling method is this?

Accepted Answer

Cluster sampling

Question 7

Which of the following best describes a double-blind experiment?

Accepted Answer

Neither the participants nor the experimenters know who is receiving the treatment.

Question 8

Given a data set with a mean of $$50$$ and a standard deviation of $$5$$, what is the z-score for a value of $$60$$?

Accepted Answer

$$z = \frac{60-50}{5} = 2$$

Question 9

Which of the following measures of center is resistant to outliers?

Accepted Answer

Median

Question 10

If a data set is bell-shaped, approximately what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

$$95\%$$

Question 11

Given the five-number summary: $$\{10, 20, 30, 40, 50\}$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 40 - 20 = 20$$

Question 12

A boxplot is constructed from a five-number summary. Which of the following is NOT included in the five-number summary?

Accepted Answer

Mean

Question 13

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.4$$, and $$A$$ and $$B$$ are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.3 + 0.4 = 0.7$$

Question 14

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

$$P = \frac{3}{8}$$

Question 15

Which of the following statements about the linear correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 16

A scatterplot shows a strong negative linear relationship. Which of the following values of $$r is $$most likely?

Accepted Answer

$$r = -0.92$$

Question 17

Which of the following is an example of a categorical variable at the nominal level of measurement?

Accepted Answer

Type of car (sedan, SUV, truck)

Question 18

A researcher wants to estimate the average height of all students at a university. She randomly selects 10 students from each class year (freshman, sophomore, junior, senior). What sampling method is she using?

Accepted Answer

Stratified sampling

Question 19

Which of the following is TRUE about the difference between an observational study and an experiment?

Accepted Answer

In an experiment, the researcher manipulates variables; in an observational study, the researcher does not.

Question 20

If two events $$A$$ and $$B$$ are independent, which of the following is TRUE?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Essential Study Guide for Introductory Statistics: Key Concepts, Definitions, and Applications

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