Question

students in 7th and 8th grade were asked the types of movies they prefer. the results of the survey are shown in the two - way table. which statements are correct? check all that apply. more 7th graders were surveyed than 8th graders. the marginal relative frequency for action movies is 44%. the joint relative frequency for 8th graders who like comedy movies is 16%. most students prefer drama movies. half of the 7th graders prefer action movies. drama 11% 15% 26% action 25% 19% 44% comedy 14% 16% 30% total 50% 50% 100%

Explanation:

Step1: Analyze number of surveyed students

The total percentage for 7th - graders is 50% and for 8th - graders is 50%, so the number of 7th - graders and 8th - graders surveyed is the same. So the statement "More 7th graders were surveyed than 8th graders" is false.

Step2: Check marginal relative frequency for action movies

The marginal relative frequency for action movies is the sum of the 7th - grade and 8th - grade percentages for action movies, which is \(25\%+19\% = 44\%\). So the statement "The marginal relative frequency for action movies is 44%" is true.

Step3: Check joint relative frequency for 8th - graders who like comedy movies

The joint relative frequency for 8th - graders who like comedy movies is 16%. So the statement "The joint relative frequency for 8th - graders who like comedy movies is 16%" is true.

Step4: Compare preferences for movie types

The percentage of students who prefer action movies is 44%, for drama is 26%, and for comedy is 30%. So most students prefer action movies, not drama movies. So the statement "Most students prefer drama movies" is false.

Step5: Check preference of 7th - graders for action movies

The percentage of 7th - graders who prefer action movies is 25%, not 50%. So the statement "Half of the 7th - graders prefer action movies" is false.

Answer:

The marginal relative frequency for action movies is 44%.
The joint relative frequency for 8th - graders who like comedy movies is 16%.