Q: Suppose the regression equation for predicting blood pressure ($$y) $$from age ($$x) is$$ $$y = 90 + 0.5x. $$What is the predicted blood pressure for a 40-year-old?

$$y = 90 + 0.5 \times 40 = 110$$

Question 1

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

Accepted Answer

Changing the order of the variables does not change $$r.$$

Question 2

A researcher finds a correlation coefficient $$r = 0.02$$ between hours studied and exam scores. What does this imply?

Accepted Answer

There is no linear association between hours studied and exam scores.

Question 3

Which of the following best describes the meaning of the slope in a regression line?

Accepted Answer

The change in the predicted response variable for each one-unit increase in the explanatory variable.

Question 4

Which scenario best illustrates the concept that 'correlation is not causation'?

Accepted Answer

A study finds a strong correlation between ice cream sales and drowning incidents.

Question 5

Suppose the regression equation for predicting blood pressure ($$y) $$from age ($$x) is$$ $$y = 90 + 0.5x. $$What is the predicted blood pressure for a 40-year-old?

Accepted Answer

$$y = 90 + 0.5 	imes 40 = 110$$

Question 6

Which of the following is NOT a property of the correlation coefficient $$r$$?

Accepted Answer

$$r$$ can be greater than $$1$$ for strong associations.

Question 7

A scatterplot shows a nonlinear association between two variables. Which of the following is TRUE?

Accepted Answer

The correlation coefficient $$r$$ may be close to zero even if there is a strong nonlinear association.

Question 8

Which of the following is an example of a discrete outcome in probability?

Accepted Answer

The number of heads in 10 coin tosses.

Question 9

In probability, what is the complement of an event $$A$$?

Accepted Answer

The event that $$A$$ does not occur.

Question 10

A bag contains 5 red balls and 7 blue balls. If you draw one ball at random, what is the probability it is red?

Accepted Answer

$$\frac{5}{12}$$

Question 11

Which of the following is TRUE about mutually exclusive events?

Accepted Answer

The probability of both occurring is zero.

Question 12

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are independent, what is the probability that both $$A$$ and $$B$$ occur?

Accepted Answer

$$0.15$$

Question 13

Which of the following best describes a probability distribution function (pdf)?

Accepted Answer

A function that assigns a probability to each possible outcome of a random variable.

Question 14

The area under the curve of a probability density function (pdf) for a continuous random variable is:

Accepted Answer

$$1$$

Question 15

Which of the following is NOT a property of the Normal distribution?

Accepted Answer

It is always skewed to the right.

Question 16

A test score is at the 90th percentile of a Normal distribution. What does this mean?

Accepted Answer

The score is higher than 90% of all scores.

Question 17

If a random variable $$X$$ has mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, what is the $$z-$$score for $$X = 60$$?

Accepted Answer

$$z = 2$$

Question 18

Which of the following is an example of a simulation in probability?

Accepted Answer

Using a computer to model the spread of a disease in a population.

Question 19

A Venn diagram is most useful for illustrating:

Accepted Answer

The relationship between mutually exclusive and overlapping events.

Study Guide: Regression, Probability, and the Normal Model in Statistics

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