**Hypothesis Testing: Finding the Critical Value**In this example, we will explore a situation involving hypothesis testing. We are given the following conditions:- Null Hypothesis (\(H_0\)): \(\mu = 100\)- Alternative Hypothesis (\(H_a\)): \(\mu > 100\)- Significance Level (\(\alpha\)): 0.05- Sample Size (\(n\)): 32The challenge is to determine the critical value that forms the rejection region for this hypothesis test.**Choices Provided:**1. \( \boxed{z = 1.645} \)2. \( \boxed{z = 1.960} \)3. \( \boxed{t = 1.960} \)4. \( \boxed{t = 1.645} \)In hypothesis testing for a population mean, the critical value determines the threshold at which we reject the null hypothesis in favor of the alternative hypothesis. The choice of \(z\)-score or \(t\)-score depends on the sample size and whether the population standard deviation is known.**Explanation of Choices:**- \(z\)-scores are typically used when the sample size is large (usually \(n \geq 30\)) and/or the population standard deviation is known.- \(t\)-scores are used when the sample size is small and/or the population standard deviation is unknown.Given:- The sample size here is 32, which is typically considered large enough to use the \(z\)-distribution.Since we are performing a one-tailed test at \(\alpha = 0.05\), the critical \(z\)-value that corresponds to this significance level (5%) in a standard normal distribution is approximately 1.645.Therefore, the appropriate critical value for this scenario is:\[ \boxed{z = 1.645} \]In conclusion, the value \(z = 1.645\) forms the rejection region for this hypothesis test, meaning that if the test statistic exceeds 1.645, we reject the null hypothesis in favor of the alternative hypothesis.

Given information Sample size n = 32 Significance level (α) = 0.05 Null and Alternative Hypothesis…

Answered: We have this situation: Ho: H = 100 H:…

Math

Statistics

We have this situation: Ho: H = 100 H: H > 100 a = 0.05 n = 32 What critical value forms the rejection region?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: The rate at which the total average of COVID cases is dx = 1 tent per day, given dt increasing at x = 10 tents and than if 25 tents are built, the average number of COVID cases per tent will be 6 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding.
%97 l1. lu. F : O Students == 03- Chapter... -> Mr. Mu Page 11] Calculus II the Chain Rule mple (9] Find (dy/dx) if y² –x² – sinxy = 0 2 Solution Exercises 3-4 dw at the given value of t : dt H.W 1-Evaluate 2 1) – W =x +y x = cost y = sint 2 2) – w =x+y x = cost + sint y = cost – sint 3) – y x = cos t y = sin?t W =-+ Z = z = 4Vi 2 4) - w = In(x²+y+z²) X = cost y = sint 5) w =2ye* – In z x = In (1 ² +1) y = tan-t z =e' t-1 6)- w =z - sinxy x =t y = Int z =e'- II >
III. Illustrate the rejection region given the critical value and identify if the t-values lie in the non-rejection region or rejection region. 1. critical t-value of -2.086 computed t-value of -2.096 2. critical t-value of ±1.071 computed t-value of 1.01
MIS. J.YU, 2.9023, V.03040 10. -0.2t The bacteria concentration in reservoir varies as C=3e-1.4t +e Using Newton-Raphson method, calculate the time required for the bacteria concentration to be 0.7. Ans. 2.488459
dy 3; find dt dx when x = 2. dt Related Rates: Given y = x³ – 2x and -
Ho p > 28 Η με 28 n3D22 D. a= 0.0005 Find the critical value of t. (Type 3 decimal places)