Math Problem Statement
Solution
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textThe image contains a question about hypothesis testing. Here's a breakdown of the problem:
- You're performing a hypothesis test for the null hypothesis against an alternative hypothesis.
- The sample consists of 25 people.
- The population follows a normal distribution .
- The power of the test at an alternative value of 15 is 58.71%.
The question asks you to find the new power (or distinguishing power) when the alternative hypothesis shifts by 0.4828 more than the original alternative value (i.e., ).
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Math Problem Analysis
Mathematical Concepts
Hypothesis testing
Normal distribution
Power of a test
Formulas
Z-score formula: \( Z = \frac{X - \mu}{\sigma / \sqrt{n}} \)
Power of a test formula using the cumulative distribution function (CDF)
Theorems
Properties of the normal distribution
Concept of statistical power
Suitable Grade Level
Undergraduate (Statistics/Probability)
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