3. A sample of size n = 16 is to be taken from a distribution that can reasonably be assumed to be Normal with a standard deviation σ of 100. The null hypothesis H0 : µ = 500 is to be tested against the alternative hypothesis H1 : µ = 520. What is the power of the .10 level test ? Choose the correct answer below and explain. (A) .315 (B) .50 (C) .60 (D) .70 ### Sample Size Calculation#### Question 10:**Problem Statement:** Compute the sample size $ n $ needed for $ \mu_1 = 520 $, $ \beta = 0.2 $, and $ \alpha = 0.05 $.\[ n = \sigma^2 \ast (z_\alpha + z_\beta)^2 / (\mu_1 - \mu_0)^2 \]Given:\[ \sigma = 100 \]\[ z_\alpha = 1.645 \]\[ z_\beta = 0.842 \]\[ \mu_0 = 20^2 \]Calculate $ n $:\[ n = 100^2 \ast (1.645 + 0.842)^2 / (20^2) =? \]Options:(A) 16(B) 32(C) 68(D) 155#### Question 11:**Problem Statement:** Compute the sample size $ n $ needed for $ \mu_1 = 510 $, $ \beta = 0.5 $, and $ \alpha = 0.05 $.\[ n = \sigma^2 \ast (z_\alpha + z_\beta)^2 / (\mu_1 - \mu_0)^2 \]Given:\[ \sigma = 100 \]\[ z_\alpha = 1.645 \]\[ z_\beta = 0.000 \]\[ \mu_0 = 20^2 \]Calculate $ n $:\[ n = 100^2 \ast (1.645 + 0.000)^2 / (20^2) =? \]Options:(A) 16(B) 32(C) 68(D) 155### Explanation of Equations and Constants:- **Sample Size ($ n $)**: The number of observations in the sample required to achieve a certain level of statistical power.- **Population Mean ($ \mu $)**: The average value of the population from which the sample is drawn.- **Beta ($ \beta $)**: The probability of Type II error (failing to reject a false null hypothesis).- **Alpha ($ \alpha $)**: The probability of Type I error (rejecting a true null hypothesis).- **Standard Deviation ($ \sigma $)**: A

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sample of size n = 16 is to be taken from a distribution that can reasonably be assumed to be Normal with a standard deviation σ of 100. The null hypothesis H0 : µ = 500 is to be tested against the alternative hypothesis H1 : µ = 520. What is the power of the .10 level test ? Choose the correct answer below and explain.

sample of size n = 16 is to be taken from a distribution that can reasonably be assumed to be Normal with a standard deviation σ of 100. The null hypothesis H0 : µ = 500 is to be tested against the alternative hypothesis H1 : µ = 520. What is the power of the .10 level test ? Choose the correct answer below and explain.

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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