Q: A regression line is given by $$\hat{y} = 3 + 2x. $$What is the predicted value of $$y$$ when $$x = 4$$?

$$\hat{y} = 3 + 2 \times 4 = 11$$

Question 1

A researcher collects data on the number of hours students study per week (quantitative) and their major (categorical: STEM or non-STEM). Which of the following best describes how to summarize the distribution of the quantitative variable?

Accepted Answer

Describe the shape, center, variability, and note any outliers using a histogram or box plot.

Question 2

Which of the following statements about the mean and median is TRUE?

Accepted Answer

The mean is not resistant to outliers, while the median is.

Question 3

A dataset of annual incomes is strongly skewed to the right. Which measure of center and variability should you use to best describe the data?

Accepted Answer

Median and interquartile range (IQR)

Question 4

Given the five-number summary: minimum = 12, $$Q_1 = 18$, median = 25, Q_3$ = 32$$, maximum = 45, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 32 - 18 = 14$$

Question 5

A value is considered a high outlier if it is greater than which of the following?

Accepted Answer

$$Q_3 + 1.5$$ 	imes IQR$$

Question 6

In a bell-shaped distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, approximately what proportion of values are between $$40$$ and $$60$$?

Accepted Answer

About 95%

Question 7

A student scored 85 on a test where the mean was 75 and the standard deviation was 5. What is the student's $$z-$$score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 8

Which of the following best describes a strong negative linear association between two quantitative variables?

Accepted Answer

Correlation coefficient close to $$-1$$

Question 9

A regression line is given by $$\hat{y} = 3 + 2x. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 3 + 2 	imes 4 = 11$$

Question 10

In a scatter plot, the explanatory variable is placed on which axis?

Accepted Answer

Horizontal axis (x-axis)

Question 11

If a value has a $$z-$$score of $$-2.5$$, what does this indicate?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 12

Which of the following is NOT a property of standard deviation?

Accepted Answer

Standard deviation is resistant to outliers.

Question 13

A two-way table is used to summarize the distribution of:

Accepted Answer

Two categorical variables

Question 14

In a study, the sample mean is 20, the sample standard deviation is 4, and a value in the sample is 28. What is the $$z-$$score for this value?

Accepted Answer

$$z = \frac{28 - 20}{4} = 2$$

Question 15

Which visual display is best for identifying the shape of a quantitative variable's distribution?

Accepted Answer

Histogram

Question 16

If the points in a scatter plot are equally scattered above and below the horizontal line at the mean of $$y$$, what does this suggest about the association between $$x$$ and $$y$$?

Accepted Answer

There is no association.

Question 17

Which of the following best describes the residual for a point $$(x, y) in $$regression?

Accepted Answer

The difference between the observed response and the predicted response: $$y - \hat{y}$$

Question 18

Which scenario is most likely to require the use of column proportions in a two-way table?

Accepted Answer

Determining if two categorical variables are associated

Question 19

A box plot shows a right whisker extending from $$Q_3 to $$the highest value not a high outlier. What does this indicate?

Accepted Answer

The right whisker extends to the highest value that is not classified as a high outlier

Chapter 2: Data Description – Essential Concepts and Applications

Guida di studio - Domande di pratica

Study guide - Flashcard