Math Problem Statement

If the null and alternative hypotheses are

Then the test is left-tailed two-tailed right-tailed

Solution

To determine the type of test (left-tailed, two-tailed, or right-tailed), we need to examine the null hypothesis (denoted as H0H_0) and the alternative hypothesis (denoted as H1H_1).

  • Left-tailed test: This occurs when the alternative hypothesis claims that a parameter is less than the null hypothesis value, i.e., H1:θ<θ0H_1: \theta < \theta_0.
  • Right-tailed test: This occurs when the alternative hypothesis claims that a parameter is greater than the null hypothesis value, i.e., H1:θ>θ0H_1: \theta > \theta_0.
  • Two-tailed test: This occurs when the alternative hypothesis claims that a parameter is not equal to the null hypothesis value, i.e., H1:θθ0H_1: \theta \neq \theta_0.

Without seeing the explicit null and alternative hypotheses, the test type can't be identified definitively. If you provide the hypotheses, I can specify which test applies.

Would you like further clarification, or do you have the hypotheses you'd like to provide? Here are some related questions to explore:

  1. What are the steps in hypothesis testing?
  2. What is a p-value, and how does it relate to these tests?
  3. What are Type I and Type II errors in hypothesis testing?
  4. How do you interpret the results of a left-tailed test?
  5. What is the difference between a z-test and a t-test?

Tip: Always carefully define the null and alternative hypotheses before deciding on the test type.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Statistical Inference

Formulas

Hypotheses Formulation (H₀ and H₁)

Theorems

Hypothesis Testing Theorem
Left-tailed, Right-tailed, and Two-tailed Tests

Suitable Grade Level

College Level Statistics