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 ) and the alternative hypothesis (denoted as ).
- Left-tailed test: This occurs when the alternative hypothesis claims that a parameter is less than the null hypothesis value, i.e., .
- Right-tailed test: This occurs when the alternative hypothesis claims that a parameter is greater than the null hypothesis value, i.e., .
- Two-tailed test: This occurs when the alternative hypothesis claims that a parameter is not equal to the null hypothesis value, i.e., .
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:
- What are the steps in hypothesis testing?
- What is a p-value, and how does it relate to these tests?
- What are Type I and Type II errors in hypothesis testing?
- How do you interpret the results of a left-tailed test?
- 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
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