https://file.aiquickdraw.com/mathbot/file/17295696783263z4jkq89.jpg

The question asks whether reducing the confidence level from 90% to 80% will make the confidence interval narrower.

### Key concepts:
- A **confidence interval** gives a range within which we expect the true population parameter (like the mean, \(\mu\)) to lie, based on sample data.
- The **confidence level** indicates how sure we are that this range contains the true population mean.
  - A **higher confidence level** (e.g., 90%, 95%) results in a **wider interval**, because we want to be more confident, so the range must be broader.
  - A **lower confidence level** (e.g., 80%) results in a **narrower interval**, because we're willing to accept less certainty and thus can use a smaller range.

### Answer:
The statement is **True**. When the confidence level decreases from 90% to 80%, the confidence interval will become narrower because we need less certainty, and thus the interval can be reduced.

Would you like a more detailed explanation or examples?

Here are 5 related questions to expand on this concept:
1. What happens to the confidence interval when the sample size increases?
2. How does the confidence interval change if the population standard deviation is unknown?
3. Why does a higher confidence level result in a wider interval?
4. Can we ever have a 100% confidence interval, and if so, what would it look like?
5. How does the width of the confidence interval affect the precision of an estimate?

**Tip:** Always remember, a lower confidence level means we accept a greater chance of error, so the confidence interval shrinks accordingly.

A 90% confidence interval estimate for a population mean μ (mu) is determined to be 72.8 to 79.6. If the confidence level is reduced to 80%, the confidence interval for μ (mu) becomes narrower.

Understand how reducing the confidence level from 90% to 80% affects the width of a confidence interval. Explore key statistical concepts like confidence intervals and population means in this Grade 11-12 level problem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation