Question

a survey was conducted to see what kinds of activities high school and college students liked best. the table shows the results of the survey.

	bowling	hiking	swimming	total
college	10	14	16	40
total	18	26	26	70

choose two correct conclusions using the results of the survey.

• a. students in high school were more likely to prefer bowling than students in college.
• b. students in high school were more likely to prefer swimming than students in college.
• c. students who prefer bowling were more likely to be in college than students who prefer hiking.
• d. students who prefer swimming were more likely to be in high school than students who prefer hiking.

Explanation:

To solve this, we calculate the conditional probabilities for each option:

For Option A:

• Probability high school students prefer bowling: $\frac{8}{30} \approx 0.267$
• Probability college students prefer bowling: $\frac{10}{40} = 0.25$

Since $0.267 > 0.25$, high school students are more likely to prefer bowling. So A is correct.

For Option B:

• Probability high school students prefer swimming: $\frac{10}{30} \approx 0.333$
• Probability college students prefer swimming: $\frac{16}{40} = 0.4$

Since $0.333 < 0.4$, high school students are not more likely to prefer swimming. So B is incorrect.

For Option C:

• Probability bowling - preferring students are in college: $\frac{10}{18} \approx 0.556$
• Probability hiking - preferring students are in college: $\frac{14}{26} \approx 0.538$

Since $0.556 > 0.538$, bowling - preferring students are more likely to be in college. So C is correct.

For Option D:

• Probability swimming - preferring students are in high school: $\frac{10}{26} \approx 0.385$
• Probability hiking - preferring students are in high school: $\frac{12}{26} \approx 0.462$

Since $0.385 < 0.462$, swimming - preferring students are not more likely to be in high school. So D is incorrect.

Answer:

A. Students in high school were more likely to prefer bowling than students in college.
C. Students who prefer bowling were more likely to be in college than students who prefer hiking.