Question

interpreting a relative frequency table
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.

	movie	concert	total
11th	0.16	0.18	0.34
12th	0.24	0.09	0.33
total	0.58	0.42	1.00

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%.

Explanation:

1. Statement 1: Marginal relative frequency for 10th graders is the total for 10th grade, which is 0.33, not 0.18. So this is incorrect.
2. Statement 2: The total relative frequency for concert is 0.42, which is 42%. So 42% of students prefer a concert. This is correct.
3. Statement 3: For 11th graders, the ratio of concert to movie is \( \frac{0.18}{0.16}=\frac{9}{8} = 1.125\). For 10th graders, it's \( \frac{0.15}{0.18}=\frac{5}{6}\approx0.833\). For 12th graders, it's \( \frac{0.09}{0.24}=\frac{3}{8} = 0.375\). So 11th graders have a greater ratio. This is correct.
4. Statement 4: The total relative frequency for 10th is 0.33, 11th is 0.34, 12th is 0.33. So 11th graders were surveyed more (since 0.34 > 0.33). So this is incorrect.
5. Statement 5: The percent who prefer movie is 58% (0.58) and concert is 42% (0.42). The difference is \( 58 - 42=16\%\). This is correct.

Answer:

• 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%.