Q: If the proportion of movies that are dramas is $$0.246$$, how many dramas would you expect in a sample of 1,000 movies?

$$0.246 \times 1000 = 246$$ dramas

Q: If a proportion is $$0.0095$$, how would you express this as a count per 100,000?

$$0.0095 \times 100,000 = 950$$ per 100,000

Question 1

Which of the following best describes the sample proportion ($$\hat{p}) $$for a categorical variable?

Accepted Answer

The ratio of the number of cases in a category to the total number of cases in the sample.

Question 2

A researcher finds that 8 out of 844 Hollywood movies released from 2019 through 2023 were Westerns. What is the proportion of Westerns among these movies, expressed as a percentage?

Accepted Answer

$$\frac{8}{844} = 0.0095$$, which is $$0.95\%$$

Question 3

If the proportion of movies that are dramas is $$0.246$$, how many dramas would you expect in a sample of 1,000 movies?

Accepted Answer

$$0.246 	imes 1000 = 246$$ dramas

Question 4

Which of the following statements about converting proportions is correct?

Accepted Answer

To convert a proportion to a percentage, multiply by 100 and add the percent symbol.

Question 5

In a two-way table, what does a column proportion represent?

Accepted Answer

The proportion of the sample whose value of the column variable is the column header.

Question 6

A survey of 2,625 adults found that 363 had a high school education and agreed with the statement 'There is only one true love for each person.' What is the overall (table) proportion for this cell?

Accepted Answer

$$\frac{363}{2625} = 0.138 or$$ $$13.8\%$$

Question 7

If 41.2% of people who do not smoke use vitamins regularly and 23.3% of people who smoke use vitamins regularly, what can you conclude about the association between smoking and vitamin use?

Accepted Answer

There is an association; people who do not smoke are almost twice as likely to use vitamins regularly as people who smoke.

Question 8

Which visual display is most appropriate for showing the distribution of a single categorical variable?

Accepted Answer

Bar chart

Question 9

What is the mode of a categorical variable?

Accepted Answer

The category with the greatest proportion.

Question 10

If a proportion is $$0.0095$$, how would you express this as a count per 100,000?

Accepted Answer

$$0.0095 	imes 100,000 = 950$$ per 100,000

Question 11

Which of the following best describes how to determine if two categorical variables are associated?

Accepted Answer

Compare the column proportions for each row; if they differ greatly, the variables are associated.

Question 12

A dataset contains 844 movies, and 208 are dramas. What is the proportion of dramas, and how would you express this as a percentage?

Accepted Answer

$$\frac{208}{844} = 0.246 or$$ $$24.6\%$$

Question 13

If you want to convert a proportion to a count per 1,000, what should you do?

Accepted Answer

Multiply the proportion by 1,000.

Question 14

Which of the following is NOT a correct way to express the proportion $$0.0095$$?

Accepted Answer

95 of every 1,000 Hollywood movies

Question 15

In a two-way table, what do the cell entries represent?

Accepted Answer

Counts of cases for each combination of row and column categories.

Question 16

A sample proportion is calculated as $$\hat{p} = \frac{x}{n}. If$$ $$x = 50$$ and $$n = 200$$, what is $$\hat{p}$$?

Accepted Answer

$$\frac{50}{200} = 0.25$$

Question 17

Which of the following is a reason to use proportions instead of counts when summarizing a categorical variable?

Accepted Answer

Proportions allow for easier comparison between groups of different sizes.

Question 18

If you know the proportion of cases in a category and the sample size, how can you find the number of cases in that category?

Accepted Answer

Multiply the proportion by the sample size.

Question 19

Which of the following best describes a 100% stacked bar chart for two categorical variables?

Accepted Answer

It displays column proportions so each bar is the same height, making it easier to compare proportions.

Describing and Summarizing Categorical Data

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