Math Problem Statement

Determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed based on H0: μ = 25 and H1: μ < 25.

Solution

This is a hypothesis testing question where you need to classify the type of test based on the alternate hypothesis (H1H_1).

Explanation:

  1. Null Hypothesis (H0H_0): μ=25\mu = 25
    This states that the population mean is 25.

  2. Alternate Hypothesis (H1H_1): μ<25\mu < 25
    This states that the population mean is less than 25.

Since the alternate hypothesis uses a "less than" symbol (<<), this indicates a left-tailed test.

Answer:

The alternate hypothesis is left-tailed.


Would you like further details or have questions about hypothesis testing?

Related Questions:

  1. What does a right-tailed hypothesis test look like?
  2. How do you conduct a hypothesis test for this problem?
  3. What are the implications of selecting a left-tailed test?
  4. How does the significance level (α\alpha) affect hypothesis tests?
  5. What are the differences between one-tailed and two-tailed tests?

Tip:

In hypothesis testing, always match the inequality sign in H1H_1 to determine if the test is left-tailed, right-tailed, or two-tailed.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Statistical Inference

Formulas

Concept of left-tailed, right-tailed, and two-tailed tests

Theorems

Null and Alternate Hypothesis Definition

Suitable Grade Level

College or Advanced High School