**Hypothesis Testing Example**Consider the following hypothesis test scenario:- Null Hypothesis (H₀): μ = 50- Alternative Hypothesis (H₁): μ ≠ 50- Significance Level (α): 0.01- Test Statistic (Z): 1.23### Questions:**A)** Is H₀ rejected?**B)** If the true value of μ is 65, is the result a Type I error, a Type II error, or a correction?**Explanation:**1. **Decision Rule:** For a two-tailed test at α = 0.01, the critical values of Z are approximately ±2.575. This means we reject H₀ if the test statistic falls in the critical region: Z < -2.575 or Z > 2.575.2. **Computed Test Statistic:** Since the calculated test statistic is Z = 1.23, which does not fall into the critical region (neither less than -2.575 nor greater than 2.575), we fail to reject H₀ at the 0.01 significance level.3. **Assessing Errors:** - **Type I Error** (α): This occurs if we reject H₀ when it is true. Given we did not reject H₀, a Type I error is not possible in this case. - **Type II Error** (β): This occurs if we fail to reject H₀ when H₁ is true. Given H₁ states μ ≠ 50 and we know the true value of μ is 65, failing to reject H₀ is actually a Type II error in this scenario.This hypothesis testing example illustrates the steps to identify whether a hypothesis should be rejected and how to assess potential errors.

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Answered: A test of H₂: H=50 versus H₁M #50 is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A test of H₂: H=50 versus H₁M #50 is performed using a significance level of α = 0.01. The value of the test statistic is z = 1.23 A) is H₂ rejected? B) if the true value of mis 65, is the results a Type I error, a Type II error, or a correction ?