Question

a random sample of 184 students at south high school were surveyed on whether they would prefer going to a movie or a concert. the results are shown in the relative frequency table. which statements are correct? check all that apply. the marginal relative frequency for 10th graders is 0.18. 42% of the students prefer a concert over a movie. a greater ratio of 11th graders prefer a concert to a movie. more 12th graders were surveyed than any other grade level. the difference in the percent of students who prefer a movie over a concert is 16%. movie concert total 10th 0.18 0.15 0.33 11th 0.16 0.18 0.34 12th 0.24 0.09 0.33 total 0.58 0.42 1.00

Explanation:

Step1: Analyze 10th - graders' marginal relative frequency

The marginal relative frequency for 10th - graders is 0.33, not 0.18. So the first statement is incorrect.

Step2: Analyze students preferring concert

The total relative frequency for students preferring a concert is 0.42, which means 42% of the students prefer a concert over a movie. So the second statement is correct.

Step3: Analyze 11th - graders' preference ratio

For 11th - graders, the relative frequency of preferring a concert is 0.18 and for a movie is 0.16. Since 0.18>0.16, a greater ratio of 11th - graders prefer a concert to a movie. So the third statement is correct.

Step4: Analyze number of surveyed students per grade

The marginal relative frequencies for 10th, 11th, and 12th - graders are 0.33, 0.34, and 0.33 respectively. So no grade has more surveyed students than the others. The fourth statement is incorrect.

Step5: Analyze difference in movie - concert preference

The relative frequency of students preferring a movie is 0.58 and for a concert is 0.42. The difference is 0.58 - 0.42=0.16 or 16%. So the fifth statement is correct.

Answer:

The correct statements are:

• 42% of the students prefer a concert over a movie.
• A greater ratio of 11th - graders prefer a concert to a movie.
• The difference in the percent of students who prefer a movie over a concert is 16%.