Math Problem Statement

We testen \( \mu_0 = 10 \) of \( \mu_a > 10 \) met een steekproef van 25 mensen en we weten dat \( X \sim N(10 ; 8.9143) \). Het onderscheidingsvermogen bij een alternatieve waarde van 15 is 58.71%. Hoeveel zou het onderscheidingsvermogen bedragen als de alternatieve waarde 0.4828 meer is dan de eerste alternatieve waarde?

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 H0:μ=10H_0: \mu = 10 against an alternative hypothesis.
  • The sample consists of 25 people.
  • The population follows a normal distribution XN(10,8.9143)X \sim N(10, 8.9143).
  • 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., 15+0.482815 + 0.4828).

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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)