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iid Let Y1, Y2, Y3, . .., Y, N(µ, o²), where o² = 25 is known. 3. Suppose we collect data of size n = 16 and the MLE turns out to be u = 2 and ô? = 25. Using the result from the previous part, conduct an a = .05 level test of Ho : µ = 0 in favor of Ha : µ # 0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null? 4. Invert the a-level test you found in the previous part to construct a 95% confidence interval for u. Interpret the confidence interval.

iid Let Y1, Y2, Y3, . .., Y, N(µ, o²), where o² = 25 is known. 3. Suppose we collect data of size n = 16 and the MLE turns out to be u = 2 and ô? = 25. Using the result from the previous part, conduct an a = .05 level test of Ho : µ = 0 in favor of Ha : µ # 0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null? 4. Invert the a-level test you found in the previous part to construct a 95% confidence interval for u. Interpret the confidence interval.

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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Solve both parts 3 and 4 of the question below.

 

**Transcription and Explanation for Educational Website:** **Given Information:** Let \( Y_1, Y_2, Y_3, \ldots, Y_n \) be independent and identically distributed as \( N(\mu, \sigma^2) \), where \( \sigma^2 = 25 \) is known. --- **Questions:** **3.** Suppose we collect data of size \( n = 16 \) and the MLE turns out to be \( \hat{\mu} = 2 \) and \( \hat{\sigma}^2 = 25 \). Using the result from the previous part, conduct an \( \alpha = 0.05 \) level test of \( H_0 : \mu = 0 \) in favor of \( H_a : \mu \neq 0 \). Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null? **4.** Invert the \( \alpha \)-level test you found in the previous part to construct a 95% confidence interval for \( \mu \). Interpret the confidence interval. --- **Explanation:** In these questions, we are dealing with hypothesis testing and confidence interval construction for the mean of a normally distributed population with known variance. - **Question 3** focuses on hypothesis testing. Here, we test the null hypothesis \( H_0 \) (that the population mean \(\mu = 0\)) against the alternative hypothesis \( H_a \) (that \(\mu \neq 0\)). You'll need to calculate critical values and the rejection region, determine the p-value, and make a decision on whether to reject or fail to reject \( H_0 \). - **Question 4** deals with constructing a confidence interval for the population mean \(\mu\) using the information obtained from the hypothesis test, providing a range in which the true mean is believed to lie with a certain level of confidence (95% in this case). Interpreting this interval helps understand the precision and reliability of the estimation.
Transcribed Image Text:**Transcription and Explanation for Educational Website:** **Given Information:** Let \( Y_1, Y_2, Y_3, \ldots, Y_n \) be independent and identically distributed as \( N(\mu, \sigma^2) \), where \( \sigma^2 = 25 \) is known. --- **Questions:** **3.** Suppose we collect data of size \( n = 16 \) and the MLE turns out to be \( \hat{\mu} = 2 \) and \( \hat{\sigma}^2 = 25 \). Using the result from the previous part, conduct an \( \alpha = 0.05 \) level test of \( H_0 : \mu = 0 \) in favor of \( H_a : \mu \neq 0 \). Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null? **4.** Invert the \( \alpha \)-level test you found in the previous part to construct a 95% confidence interval for \( \mu \). Interpret the confidence interval. --- **Explanation:** In these questions, we are dealing with hypothesis testing and confidence interval construction for the mean of a normally distributed population with known variance. - **Question 3** focuses on hypothesis testing. Here, we test the null hypothesis \( H_0 \) (that the population mean \(\mu = 0\)) against the alternative hypothesis \( H_a \) (that \(\mu \neq 0\)). You'll need to calculate critical values and the rejection region, determine the p-value, and make a decision on whether to reject or fail to reject \( H_0 \). - **Question 4** deals with constructing a confidence interval for the population mean \(\mu\) using the information obtained from the hypothesis test, providing a range in which the true mean is believed to lie with a certain level of confidence (95% in this case). Interpreting this interval helps understand the precision and reliability of the estimation.
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