According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010-11 (Time, October 31, 2011). Arandom sample of 455 of this year's graduates showed that their average such debt is $39,000 with a standarn deviation of $5520. Do the data provide significant evidence at a 5% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both the p-value approach and the critical-value approach. Use the p-value approach. Use the t distribution table to find a range for the p-value. Enter the exact values for the range.

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**Title: Statistical Analysis of College Graduate Debt**

**Overview:**

According to an estimate, the average total parent and student debt for new college graduates was $34,400 in the 2010-11 academic year (Time, October 31, 2011). A study was conducted using a random sample of 455 graduates from the current year. The sample showed an average debt of $39,000 with a standard deviation of $5520. The goal is to determine if there is significant evidence at a 5% significance level to support the claim that the current average debt is higher than $34,400. Two approaches are used: the p-value approach and the critical-value approach.

**1. P-value Approach:**
- Use the t-distribution table to find a range for the p-value.
- Enter the exact values for this range:

   - \(i\) \< p-value \< \(i\)

**2. Critical-value Approach:**
- Round the observed value to four decimal places.
- The critical value should be rounded to two decimal places.

   - Observed value = \(i\)
   - Critical value = 

**Conclusion:**
- Determine whether the current average total parent and student debt for new graduates is "not higher than" or "higher than" $34,400. Use the provided selection menu to conclude:

   - Conclusion: The current average total parent and student debt for new graduates is \(\_\_\_\_\_\_\_\_\_\_\) $34,400.

**Note:** This section could include interactive elements, such as drop-down menus and input fields, to engage students in the decision-making process.
Transcribed Image Text:**Title: Statistical Analysis of College Graduate Debt** **Overview:** According to an estimate, the average total parent and student debt for new college graduates was $34,400 in the 2010-11 academic year (Time, October 31, 2011). A study was conducted using a random sample of 455 graduates from the current year. The sample showed an average debt of $39,000 with a standard deviation of $5520. The goal is to determine if there is significant evidence at a 5% significance level to support the claim that the current average debt is higher than $34,400. Two approaches are used: the p-value approach and the critical-value approach. **1. P-value Approach:** - Use the t-distribution table to find a range for the p-value. - Enter the exact values for this range: - \(i\) \< p-value \< \(i\) **2. Critical-value Approach:** - Round the observed value to four decimal places. - The critical value should be rounded to two decimal places. - Observed value = \(i\) - Critical value = **Conclusion:** - Determine whether the current average total parent and student debt for new graduates is "not higher than" or "higher than" $34,400. Use the provided selection menu to conclude: - Conclusion: The current average total parent and student debt for new graduates is \(\_\_\_\_\_\_\_\_\_\_\) $34,400. **Note:** This section could include interactive elements, such as drop-down menus and input fields, to engage students in the decision-making process.
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