Q: In a contingency table, which calculation would you use to find the conditional distribution of 'Speeding Violation' given 'Uses Cell Phone While Driving'?

$$\frac{\text{cell frequency}}{\text{row total}}$$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that displays the frequency distribution of variables and shows the relationship between two categorical variables.

Question 2

Given a contingency table with two categorical variables, how do you calculate the marginal distribution for one variable?

Accepted Answer

Sum the frequencies across the levels of the other variable for each category of the variable of interest.

Question 3

In a contingency table, what is the formula for calculating the relative frequency of a cell?

Accepted Answer

Divide the frequency in the cell by the overall total: $$\frac{	ext{cell frequency}}{	ext{overall total}}$$

Question 4

Suppose a contingency table shows the following data for cell phone use and speeding violations: 25 people used a cell phone and had a speeding violation, 280 used a cell phone and did not have a violation, 45 did not use a cell phone and had a violation, and 405 did not use a cell phone and did not have a violation. What is the relative frequency of people who used a cell phone and had a speeding violation, given the total sample size is 755?

Accepted Answer

$$\frac{25}{755} \approx 0.0331$$

Question 5

How do you construct a conditional distribution for a column variable in a contingency table?

Accepted Answer

Divide each cell in the column by the column total: $$\frac{	ext{cell frequency}}{	ext{column total}}$$

Question 6

A survey of 135 students found 60 right-handed males, 15 left-handed males, 45 right-handed females, and 15 left-handed females. What is the marginal distribution of right-handed students?

Accepted Answer

$$\frac{60 + 45}{135} = \frac{105}{135} \approx 0.778$$

Question 7

If you want to find the probability that a randomly selected respondent is Hispanic and has 'No Opinion' about a policy, given a total of 785 respondents and 34 Hispanic respondents with 'No Opinion', what is the correct calculation?

Accepted Answer

$$\frac{34}{785} \approx 0.0433$$

Question 8

Which of the following statements about marginal distributions is TRUE?

Accepted Answer

Marginal distributions summarize the totals for one variable, ignoring the other variable.

Question 9

In a contingency table, which calculation would you use to find the conditional distribution of 'Speeding Violation' given 'Uses Cell Phone While Driving'?

Accepted Answer

$$\frac{	ext{cell frequency}}{	ext{row total}}$$

Question 10

A table shows 81 males and 54 females. Of the males, 66 are right-handed and 15 are left-handed. Of the females, 45 are right-handed and 9 are left-handed. What is the conditional probability that a student is right-handed given that the student is male?

Accepted Answer

$$\frac{66}{81} \approx 0.815$$

Question 11

Why is it important to use relative frequencies when comparing groups of different sizes in a contingency table?

Accepted Answer

Relative frequencies standardize the data, allowing for meaningful comparisons between groups regardless of their size.

Question 12

Given a contingency table, which step is necessary to construct a relative frequency marginal distribution?

Accepted Answer

Divide each row and column total by the overall total.

Question 13

A survey asks respondents if they think a policy is a 'Good thing', 'Bad thing', 'Good and Bad', or have 'No Opinion'. If 160 white respondents say 'Good thing' out of 302 total white respondents, what is the conditional probability that a white respondent thinks the policy is a 'Good thing'?

Accepted Answer

$$\frac{160}{302} \approx 0.530$$

Question 14

Which of the following is NOT a correct use of a contingency table?

Accepted Answer

To calculate the mean and standard deviation of a continuous variable.

Question 15

If you have a contingency table with row totals and column totals, what does the intersection cell represent?

Accepted Answer

The joint frequency of the two categories represented by that row and column.

Question 16

A table shows 45 females are right-handed and 9 are left-handed. What is the marginal distribution of left-handed females?

Accepted Answer

$$\frac{9}{135} \approx 0.067$$

Question 17

Which calculation would you use to find the relative frequency of 'No speeding violation' among those who do not use a cell phone while driving, given 405 such cases out of 450 total 'No speeding violation' cases?

Accepted Answer

$$\frac{405}{450} \approx 0.900$$

Question 18

If you want to compare the likelihood of speeding violations between cell phone users and non-users, which distribution should you use?

Accepted Answer

Conditional distribution of speeding violations given cell phone use.

Question 19

Which of the following best describes a conditional distribution?

Accepted Answer

A distribution that shows the probability of one variable given a specific value of another variable.

Contingency Tables, Marginal Distributions, and Conditional Distributions in Statistics

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