Q: A dataset has the following five-number summary: Min = 10, Q1 = 20, Median = 30, Q3 = 40, Max = 100. Using the 1.5IQR rule, which value is an outlier?

$$100 is an $$outlier because $$100 \u003e Q3 + 1.5 \times (Q3 - Q1)$$

Q: Given the following contingency table for a survey of 100 people: - 40 like coffee only - 30 like tea only - 10 like both - 20 like neither What is the probability that a randomly selected person likes coffee (only or both)?

$$P(\text{coffee}) = \frac{40 + 10}{100} = 0.5$$

Question 1

A pharmaceutical company wants to estimate the average recovery time for a new drug. They only survey patients from a single hospital known for faster recoveries. Which type of bias is most likely present in their sampling method?

Accepted Answer

Selection bias

Question 2

A histogram of exam scores is shown to be skewed right. Which of the following best describes the relationship between the mean and the median?

Accepted Answer

The mean is greater than the median.

Question 3

A bar graph displays the number of car accidents per month, but the vertical axis starts at 50 instead of 0. What is the main issue with this graph, and how can it be fixed?

Accepted Answer

It is misleading because it exaggerates differences; fix by starting the axis at 0.

Question 4

Suppose two normal distributions are shown: Distribution A has mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, and Distribution B has mean $$\mu = 60$$ and standard deviation $$\sigma = 10. $$Which statement is correct?

Accepted Answer

Distribution B is centered further to the right and is more spread out than Distribution A.

Question 5

A dataset has the following five-number summary: Min = 10, Q1 = 20, Median = 30, Q3 = 40, Max = 100. Using the 1.5IQR rule, which value is an outlier?

Accepted Answer

$$100 is an $$outlier because $$100 \u003e Q3 + 1.5 	imes (Q3 - Q1)$$

Question 6

A student scored at the 90th percentile on a standardized test. What does this mean?

Accepted Answer

The student scored higher than 90% of the test-takers.

Question 7

Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 14$$

Question 8

A scatterplot shows a strong, negative linear relationship between two variables. Which of the following is the most likely value for the correlation coefficient $$r$$?

Accepted Answer

$$r = -0.85$$

Question 9

If the correlation coefficient $$r = 0.6$$, what is the coefficient of determination $$R^2$$ and what does it represent?

Accepted Answer

$$R^2 = 0.36$, which means 36\% of the variation in y$ is explained by x$.

Question 10

A regression model predicts a house price of $$\250$$,000$$ for a certain size, but the actual price is $$\$$270,000. $$What is the residual?

Accepted Answer

$$\20$$,000$

Question 11

A researcher uses a regression equation to predict values far outside the range of the observed data. What is this practice called, and why is it problematic?

Accepted Answer

Extrapolation; predictions may not be reliable outside the observed range.

Question 12

Given the following contingency table for a survey of 100 people:

- 40 like coffee only
- 30 like tea only
- 10 like both
- 20 like neither

What is the probability that a randomly selected person likes coffee (only or both)?

Accepted Answer

$$P(	ext{coffee}) = \frac{40 + 10}{100} = 0.5$$

Question 13

Which of the following is the correct general addition rule for two events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 14

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \mid B)$$?

Accepted Answer

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.2}{0.5} = 0.4$$

Question 15

A bag contains 3 red, 2 blue, and 1 green marble. If you draw one marble at random, what is the sample space?

Accepted Answer

$$\{ 	ext{red}, 	ext{blue}, 	ext{green} \}$$

Question 16

In a survey, 60 people like apples, 40 like oranges, and 20 like both. What is the probability that a randomly selected person likes either apples or oranges?

Accepted Answer

$$P(	ext{apples or oranges}) = \frac{60 + 40 - 20}{100} = 0.8$$

Question 17

Which of the following best describes a marginal probability in a contingency table?

Accepted Answer

The probability of a single event occurring, regardless of other events.

Question 18

A boxplot shows the median closer to Q1 than Q3. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed right.

Question 19

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$Using the empirical rule, what percentage of data falls between $$85$$ and $$115$$?

Accepted Answer

$$68\%$$

Essential Study Notes for Introductory Statistics: Data, Distributions, and Probability

Guida di studio - Domande di pratica

Study guide - Flashcard