Math Problem Statement

A researcher believes that average student debt is more than $25,000. Assume that the population standard deviation is $5,000.

a. What is the mean student debt of the sample?

Solution

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Population Mean
Standard Deviation
Normal Distribution

Formulas

z = (x̄ - μ) / (σ / √n)
Null hypothesis (H₀): μ = 25,000
Alternative hypothesis (Hₐ): μ > 25,000

Theorems

Central Limit Theorem
Z-Test for One Mean

Suitable Grade Level

College-level Statistics