During a particular year, 77 graduating boys chose to attend a 4-year college, while 34 boys attended a 2-year college; 83 girls chose a 4-year college, and 33 attended a 2-year college. What conclusion can be drawn?

Question

If you are a boy in this group, you are more likely to attend a 2-year college than a 4-year college..
If you are a girl in this group, you are more likely to attend a 2-year college than a 4-year college..
If you are a girl in this group, you are more likely to attend a 4-year college than a 2-year college..
Knowing if a person attended a 4-year college will help determine gender.

Answer 1

To analyze the data provided, we can summarize the choices made by boys and girls regarding college attendance.

For Boys:

• 4-year college: 77
• 2-year college: 34
• Total boys = 77 + 34 = 111

For Girls:

• 4-year college: 83
• 2-year college: 33
• Total girls = 83 + 33 = 116

Next, let's look at the probabilities:

Boys:

• Probability of attending a 4-year college = 77 / 111
• Probability of attending a 2-year college = 34 / 111

Calculating these probabilities:

• Probability of attending a 4-year college = 77/111 ≈ 0.693 (or 69.3%)
• Probability of attending a 2-year college = 34/111 ≈ 0.306 (or 30.6%)

Thus, boys are more likely to attend a 4-year college than a 2-year college.

Girls:

• Probability of attending a 4-year college = 83 / 116
• Probability of attending a 2-year college = 33 / 116

Calculating these probabilities:

• Probability of attending a 4-year college = 83/116 ≈ 0.715 (or 71.5%)
• Probability of attending a 2-year college = 33/116 ≈ 0.284 (or 28.4%)

Thus, girls are also more likely to attend a 4-year college than a 2-year college.

Conclusion: Now, let's evaluate the statements:

1. If you are a boy in this group, you are more likely to attend a 2-year college than a 4-year college. (False)
2. If you are a girl in this group, you are more likely to attend a 2-year college than a 4-year college. (False)
3. If you are a girl in this group, you are more likely to attend a 4-year college than a 2-year college. (True)
4. Knowing if a person attended a 4-year college will help determine gender. (Not necessarily true, as both genders tend to attend 4-year colleges.)

The correct conclusion based on the data is the third statement:

• If you are a girl in this group, you are more likely to attend a 4-year college than a 2-year college.