Question 1

Given the contingency table below, what is the conditional proportion of organic foods that contain pesticides?

Organic: 29 (Yes), 98 (No), Total = 127

Use the formula $$	ext{Conditional Proportion} = \frac{	ext{Count in cell}}{	ext{Row total}}.$$

Accepted Answer

$$\frac{29}{127} = 0.23$$

Question 2

Which variable is the response variable in the study of food type and pesticide status?

Accepted Answer

Pesticide status

Question 3

What does it mean if there is no association between food type and pesticide status in the contingency table?

Accepted Answer

The proportions of pesticide presence are the same for both food types.

Question 4

A scatterplot is used to display the relationship between which types of variables?

Accepted Answer

Two quantitative variables

Question 5

Which of the following best describes a positive association in a scatterplot?

Accepted Answer

As $$x$$ increases, $$y$$ tends to increase.

Question 6

Given the formula for the correlation coefficient:

$$ r = \frac{1}{n-1} \sum_{i=1}^n \left( \frac{x_i - \overline{x}}{s_x} \right) \left( \frac{y_i - \overline{y}}{s_y} \right) $$

What does a value of $$r = -0.91$$ indicate about the relationship between $$x$$ and $$y$$?

Accepted Answer

A strong negative linear relationship

Question 7

If the correlation coefficient $$r is $$calculated for the same data set but the units of $$x$$ are changed from meters to centimeters, what happens to $$r$$?

Accepted Answer

$$r$$ remains the same

Question 8

Which of the following statements about correlation is FALSE?

Accepted Answer

Correlation can be used for categorical variables.

Question 9

Suppose you have the following data for two variables:

$$x = [2, 4, 6, 8]$$, $$y = [5, 7, 9, 11].

$$What is the direction of the association?

Accepted Answer

Positive

Question 10

In a study, the correlation between time spent studying (hours) and exam score (points) is $$r = 0.85. $$Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear association between study time and exam score.

Question 11

Which of the following is a property of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$affected by outliers.

Question 12

A contingency table shows the following counts for pesticide presence:

Organic: 29 (Present), 98 (Not Present)
Conventional: 19485 (Present), 7086 (Not Present)

What is the overall proportion of foods that contain pesticides?

Use $$	ext{Proportion} = \frac{	ext{Total Present}}{	ext{Grand Total}}.$$

Accepted Answer

$$\frac{19514}{26698} \approx 0.73$$

Question 13

Which of the following best describes the use of a contingency table?

Accepted Answer

To display the association between two categorical variables

Question 14

If an outlier is present in a scatterplot, what is the most likely effect on the correlation coefficient $$r$$?

Accepted Answer

$$r$$ may be greatly increased or decreased, depending on the outlier's location.

Question 15

Which of the following is NOT a step in constructing a scatterplot using a calculator?

Accepted Answer

Calculate the mean of the explanatory variable before plotting

Question 16

A researcher finds $$r = 0$$ for two variables. What does this indicate?

Accepted Answer

There is no linear association between the variables.

Question 17

Which of the following is a correct interpretation of the conditional proportion 0.77 for organic foods in Table 3.2?

Accepted Answer

77% of organic foods sampled did not contain pesticide residues.

Question 18

Which of the following is NOT a characteristic used to describe the overall pattern of a scatterplot?

Accepted Answer

Frequency (mode, median)

Question 19

If women always marry men exactly 2 years older than themselves, what is the correlation between their ages?

Accepted Answer

$$r = 1$$

Lesson 5

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드