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### Question 8:
The question asks for the proportion of private institutions in Texas. Based on the table, for Texas:

- Total number of colleges = 262
- Number of private (nonprofit + for-profit) colleges = 71 + 84 = 155

The proportion of private institutions in Texas is:
\[
\text{Proportion} = \frac{155}{262}
\]
This matches option **A)**.

### Question 9:
The question provides a breakdown of preferences between math and English among middle and high school students. There are:
- 100 middle school students
- 200 high school students
- 180 students who prefer math and 120 who prefer English

Now, let's evaluate which two-way table correctly represents this data.

- The total number of students is 300 (100 middle school + 200 high school).
- The table should have totals that match this: 180 students for math and 120 students for English.

Now, let's check the options:
- Option **C** correctly sums up to 180 for math and 120 for English, and totals match the given numbers for middle and high school.

So, **C** is the correct answer for question 9.

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Would you like further details on how these answers were derived or have any specific questions? 

Here are five follow-up questions based on this:

1. What is the general formula for finding a proportion?
2. Can you explain how to verify whether a two-way table represents accurate data?
3. What is the difference between nonprofit and for-profit colleges?
4. How would you calculate the proportion of public colleges for California?
5. Why might it be important to compare preferences for different subjects in schools?

**Tip:** When dealing with proportions, always ensure that the sum of the parts equals the total, and cross-check for accuracy!

The National Center for Education Statistics shares data for all colleges in the United States. Here's 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 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.

Learn how to calculate the proportion of private institutions in Texas based on a provided data table and how to analyze a two-way table showing student preferences between math and English classes across different school levels. This problem includes key concepts such as proportions and data analysis.

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