Question

1. the national center for education statistics shares data for all colleges in the united states. here is the distribution of the type of college for the three states with the most colleges. for colleges in texas, what proportion of them are private institutions? a) $\frac{155}{262}$ b) $\frac{155}{659}$ c) $\frac{159}{996}$ d) $\frac{262}{996}$ e) $\frac{659}{996}$ 9. a school district surveyed students about whether they prefer math or english class and found that there was no association between school level (middle school, high school) and preferred class. the survey included 100 middle school students and 200 high school students. in total, 180 of the students preferred math and 120 preferred english. which two - way table represents this scenario? a) a two - way table with rows middle school, high school, total and columns math, english, total and values: middle school - math: 50, english: 50, total: 100; high school - math: 130, english: 70, total: 200; total - math: 180, english: 120, total: 300 b) a two - way table with rows middle school, high school, total and columns math, english, total and values: middle school - math: 40, english: 60, total: 100; high school - math: 140, english: 60, total: 200; total - math: 180, english: 120, total: 300 c) a two - way table with rows middle school, high school, total and columns math, english, total and values: middle school - math: 80, english: 20, total: 100; high school - math: 100, english: 100, total: 200; total - math: 180, english: 120, total: 300 d) a two - way table with rows middle school, high school, total and columns math, english, total and values: middle school - math: 60, english: 40, total: 100; high school - math: 120, english: 80, total: 200; total - math: 180, english: 120, total: 300 e) a two - way table with rows middle school, high school, total and columns math, english, total and values: middle school - math: 90, english: 10, total: 100; high school - math: 90, english: 80, total: 200; total - math: 180, english: 120, total: 300

Explanation:

3.

Step1: Identify private institutions in Texas

In Texas, the number of private - nonprofit colleges is 71 and the number of private for - profit colleges is 84. So the total number of private institutions in Texas is \(71 + 84=155\).

Step2: Identify total number of colleges in Texas

The total number of colleges in Texas is 262.

Step3: Calculate the proportion

The proportion of private institutions in Texas is \(\frac{155}{262}\).

Step1: Check row and column totals

We know that the total number of middle - school students is 100, the total number of high - school students is 200, the total number of students who prefer math is 180, and the total number of students who prefer English is 120.

Step2: Analyze each option

For option B:

• The sum of middle - school students: \(40 + 60=100\)
• The sum of high - school students: \(140+60 = 200\)
• The sum of students who prefer math: \(40 + 140=180\)
• The sum of students who prefer English: \(60+60 = 120\)

Answer:

A. \(\frac{155}{262}\)

9.