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and for the fixed null hypothesis Ho: Mo, let the test statistic = X - μo have a standard normal distribution when Ho is true. Give the significance level for each of the following situations: 1. The rejection region is {ê> 1.88} and Hai μ> μo : 2. The rejection region is {< -2.75} and H₁ μ< μo 3. The rejection region is {> 2.88 or < -2.88} and H₁ μμo :

and for the fixed null hypothesis Ho: Mo, let the test statistic = X - μo have a standard normal distribution when Ho is true. Give the significance level for each of the following situations: 1. The rejection region is {ê> 1.88} and Hai μ> μo : 2. The rejection region is {< -2.75} and H₁ μ< μo 3. The rejection region is {> 2.88 or < -2.88} and H₁ μμo :

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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For a sample \( X_1, X_2, \ldots, X_n \overset{\text{iid}}{\sim} N(\mu, 1) \) and for the *fixed* null hypothesis \( H_0 : \mu = \mu_0 \), let the test statistic \( \hat{\theta} = \overline{X} - \mu_0 \) have a standard normal distribution when \( H_0 \) is true. Give the significance level for each of the following situations: 1. The rejection region is \( \{\hat{\theta} > 1.88\} \) and \( H_a : \mu > \mu_0 \) 2. The rejection region is \( \{\hat{\theta} < -2.75\} \) and \( H_a : \mu < \mu_0 \) 3. The rejection region is \( \{\hat{\theta} > 2.88 \text{ or } \hat{\theta} < -2.88\} \) and \( H_a : \mu \neq \mu_0 \) --- **Hint** Hint: Significance level is just another name for \( \alpha \), the probability of type I error.
Transcribed Image Text:For a sample \( X_1, X_2, \ldots, X_n \overset{\text{iid}}{\sim} N(\mu, 1) \) and for the *fixed* null hypothesis \( H_0 : \mu = \mu_0 \), let the test statistic \( \hat{\theta} = \overline{X} - \mu_0 \) have a standard normal distribution when \( H_0 \) is true. Give the significance level for each of the following situations: 1. The rejection region is \( \{\hat{\theta} > 1.88\} \) and \( H_a : \mu > \mu_0 \) 2. The rejection region is \( \{\hat{\theta} < -2.75\} \) and \( H_a : \mu < \mu_0 \) 3. The rejection region is \( \{\hat{\theta} > 2.88 \text{ or } \hat{\theta} < -2.88\} \) and \( H_a : \mu \neq \mu_0 \) --- **Hint** Hint: Significance level is just another name for \( \alpha \), the probability of type I error.
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