Q: A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another without replacement, what is the probability that both are red? (Give your answer as a fraction.)

$$\$$\frac{5}{12} \times \frac{4}{11} = \frac{20}{132} = \frac{5}{33}\$

Q: In a survey, 60% of respondents are female and 40% are male. If 30% of females and 20% of males prefer product A, what is the probability that a randomly selected respondent prefers product A?

$$\0.3$$ \times 0.6 + 0.2 \times 0.4 = 0.18 + 0.08 = 0.26\$

Question 1

A researcher collects data on the number of hours students study per week (x) and their exam scores (y). Which variable is the explanatory variable, and which is the response variable?

Accepted Answer

x is the explanatory variable; y is the response variable.

Question 2

Suppose the correlation coefficient $$r$$ between two variables is $$-0.85. $$Which of the following best describes the association?

Accepted Answer

There is a strong negative linear association.

Question 3

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

Accepted Answer

$$\$$\hat{y} = 14\$

Question 4

Which of the following is NOT an assumption for using a linear regression model?

Accepted Answer

The explanatory variable must be categorical.

Question 5

A data point has a large residual and is far from the mean of the explanatory variable. Which of the following best describes this point?

Accepted Answer

It is an outlier with high leverage and may be influential.

Question 6

Which of the following best describes extrapolation in the context of regression analysis?

Accepted Answer

Predicting values outside the range of observed data.

Question 7

A company wants to estimate the average salary of its employees. They divide employees into departments and randomly sample from each department. What type of sampling is this?

Accepted Answer

Stratified sampling

Question 8

Which of the following is an example of response bias?

Accepted Answer

Survey questions are worded to influence answers.

Question 9

In an experiment testing a new medication, what is the 'factor'?

Accepted Answer

The variable being manipulated, such as the medication itself.

Question 10

Which of the following statements about probability is TRUE?

Accepted Answer

The probability of any event is always between $$0$$ and $$1.$$

Question 11

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are disjoint, what is $$P(A \cup B)$$?

Accepted Answer

$$\0.8$$\$

Question 12

A bag contains 5 red balls and 7 blue balls. If two balls are drawn one after another without replacement, what is the probability that both are red? (Give your answer as a fraction.)

Accepted Answer

$$\$$\frac{5}{12} 	imes \frac{4}{11} = \frac{20}{132} = \frac{5}{33}\$

Question 13

In a survey, 60% of respondents are female and 40% are male. If 30% of females and 20% of males prefer product A, what is the probability that a randomly selected respondent prefers product A?

Accepted Answer

$$\0.3$$ 	imes 0.6 + 0.2 	imes 0.4 = 0.18 + 0.08 = 0.26\$

Question 14

Which of the following best describes a census?

Accepted Answer

A study where every member of the population is surveyed.

Question 15

Which of the following is TRUE about independent events?

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 16

A Venn diagram shows that $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2. $$What is $$P(A \cup B)$$?

Accepted Answer

$$\0.4 + 0.5 - 0.2 = 0.7$$\$

Question 17

Which of the following is a property of probability?

Accepted Answer

$$\P(A^c) = 1 - P(A$$)\$$ for any event A$.

Question 18

A study follows a group of smokers for 10 years to see who develops lung cancer. What type of study is this?

Accepted Answer

Prospective observational study

Question 19

In a clinical trial, neither the subjects nor the researchers know who receives the treatment or placebo. What is this an example of?

Accepted Answer

Double blinding

Exam 2 Review Guide: Statistics Concepts (Chapters 6–8, 10–12)

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