Q: A medical researcher finds that 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 patient?

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

Question 1

Given the data set: 7, 12, 15, 18, 22, what is the median of the set?

Accepted Answer

$$15$$

Question 2

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile ($$Q_3) $$and the first quartile ($$Q_1$$): $$IQR = Q_3$ - Q_1$

Question 3

Which of the following is NOT a purpose of sampling distributions in statistics?

Accepted Answer

To calculate the median of a data set.

Question 4

A researcher wants to study the relationship between hours studied and exam scores. Which statistical concept should be used to determine the form, direction, and strength of this relationship?

Accepted Answer

Correlation

Question 5

Which equation represents the regression line for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx$$

Question 6

In a university, 600 students are enrolled in both biology and chemistry. Of these, 110 got an A in biology, 95 got an A in chemistry, and 50 got an A in both. What is the probability that a randomly chosen student got an A in biology or chemistry?

Accepted Answer

$$\frac{110 + 95 - 50}{600}$$

Question 7

Using the same scenario, what is the probability that a randomly chosen student did NOT get an A in chemistry?

Accepted Answer

$$1 - \frac{95}{600}$$

Question 8

Which of the following best describes a positive correlation between two variables?

Accepted Answer

As one variable increases, the other increases.

Question 9

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

A strong negative linear relationship.

Question 10

A medical researcher finds that 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 patient?

Accepted Answer

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

Question 11

Which of the following statements about the median is TRUE?

Accepted Answer

It is the middle value when data are ordered.

Question 12

A sample of exam scores is: 60, 70, 80, 90, 100. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 90 - 70 = 20$$

Question 13

Which of the following is a key property of a sampling distribution of the sample mean?

Accepted Answer

Its mean equals the population mean.

Question 14

If a regression line is given by $$y = 2 + 3x$$, what is the value of $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 2 + 3 	imes 5 = 17$$

Question 15

A student claims that the correlation coefficient $$r$$ can only take values between $$0$$ and $$1. Is $$this correct?

Accepted Answer

No, because $$r$$ ranges from $$-1 to$$ $$1.$$

Statistics Study Notes: Data Measures, Sampling, Correlation, Regression, and Probability

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