A high school guidance counselor has a pamphlet that says that 35% of all high school students go to a community college after graduation. In a survey of 275 randomly selected high school seniors, 116 replied that they planned to go to a community college in the fall. Use a 95% confidence interval to test and see if the pamphlet needs updating. Which of the following are true? Select all that apply.


The confidence interval we found is entirely to the right of 35%.

The confidence interval we found is entirely to the left of 35%.

The sample proportion is different from the 35% shown in the pamphlet.

The confidence interval we found contains 35%.

The sample proportion is the same as the 35% shown in the pamphlet.

Based on the confidence interval calculated, let's evaluate each statement:

1. **The confidence interval we found is entirely to the right of 35%.**

   The confidence interval is approximately \(36.3\%\) to \(48.0\%\). Since 35% is not within this range and the entire interval is greater than 35%, this statement is **true**.

2. **The confidence interval we found is entirely to the left of 35%.**

   Since the confidence interval is \(36.3\%\) to \(48.0\%\), which is entirely above 35%, this statement is **false**.

3. **The sample proportion is different from the 35% shown in the pamphlet.**

   The sample proportion is \(42.18\%\), which is different from 35%. This statement is **true**.

4. **The confidence interval we found contains 35%.**

   The confidence interval is \(36.3\%\) to \(48.0\%\), which does not include 35%. This statement is **false**.

5. **The sample proportion is the same as the 35% shown in the pamphlet.**

   The sample proportion is \(42.18\%\), which is different from 35%. This statement is **false**.

### Conclusion:

The statements that are **true** are:
- The confidence interval we found is entirely to the right of 35%.
- The sample proportion is different from the 35% shown in the pamphlet.

Would you like more details or have any questions?

Here are 5 questions you might consider next:
1. How does the sample size affect the width of the confidence interval?
2. What is the difference between a confidence interval and a hypothesis test?
3. How can the margin of error be reduced in a survey?
4. What are the implications of having a confidence interval that does not include the stated proportion?
5. How do you calculate a confidence interval for different confidence levels, like 90% or 99%?

**Tip:** When interpreting confidence intervals, it's crucial to consider both the sample size and the confidence level to ensure the results are reliable and accurate.

Explore the accuracy of a high school pamphlet stating that 35% of students plan to attend community college. Using a 95% confidence interval, evaluate if this proportion holds true based on a survey of 275 high school seniors. Analyze the survey results and the confidence interval to determine if the pamphlet needs updating.

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