Q: A data set has $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20. $$According to the $$1.5 \times IQR$$ rule, which value would be considered an outlier?

$$Q_3 + 1.5$$ \times IQR = 40 + 30 = 70$$; any value above 70 is an outlier.

Q: Given the following contingency table for 100 students: 40 like math, 30 like science, 20 like both, and 10 like neither. What is the probability that a randomly selected student likes math or science?

$$P(\text{math or science}) = \frac{40 + 30 - 20}{100} = 0.5$$

Q: A bag contains 3 red, 2 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

$$\frac{2}{10} \times \frac{1}{9} = \frac{2}{90}$$

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 this 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

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

Accepted Answer

Distribution A is taller and narrower than Distribution B.

Question 5

Suppose the heights of adult men are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. Using the empirical rule, what percentage of men are expected to be between 67 and 73 inches tall?

Accepted Answer

$$68\%$$

Question 6

Given the data set: $$2, 4, 7, 10, 12$$, what is the five-number summary?

Accepted Answer

$$2, 4, 7, 10, 12$$

Question 7

A data set has $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20. $$According to the $$1.5 	imes IQR$$ rule, which value would be considered an outlier?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR = 40 + 30 = 70$$; any value above 70 is an outlier.

Question 8

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

Accepted Answer

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

Question 9

Which of the following boxplots represents a distribution with a median closer to $$Q_1$$ than $$Q_3$$?

Accepted Answer

A boxplot where the median line is closer to the left edge of the box.

Question 10

A scatter plot shows a strong, positive, linear relationship between two variables. Which value is most likely for the correlation coefficient $$r$$?

Accepted Answer

$$r = 0.85$$

Question 11

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 is explained by the model.

Question 12

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

Accepted Answer

$$\hat{y} = 14$$

Question 13

A data point has an observed value $$y = 10$$ and a predicted value $$\hat{y} = 8. $$What is the residual?

Accepted Answer

$$2$$

Question 14

A researcher uses a regression equation to predict values far outside the range of the data. What is this practice called?

Accepted Answer

Extrapolation

Question 15

Given the following contingency table for 100 students: 40 like math, 30 like science, 20 like both, and 10 like neither. What is the probability that a randomly selected student likes math or science?

Accepted Answer

$$P(	ext{math or science}) = \frac{40 + 30 - 20}{100} = 0.5$$

Question 16

Which of the following is an example of a conditional probability?

Accepted Answer

The probability that a student is left-handed given that they are female.

Question 17

A bag contains 3 red, 2 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability that both are blue?

Accepted Answer

$$\frac{2}{10} 	imes \frac{1}{9} = \frac{2}{90}$$

Question 18

Which of the following best describes the difference between marginal and conditional probabilities in a contingency table?

Accepted Answer

Marginal probabilities refer to totals for one variable, while conditional probabilities refer to probabilities given a specific condition on another variable.

Question 19

A coin is flipped three times. What is the sample space for this experiment?

Accepted Answer

$$\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$$

MAT124 Midterm Study Guide: Key Topics in Introductory Statistics

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