### Statistical Hypothesis Testing ExampleA random sample of 100 observations from a population with a standard deviation of 39 yielded a sample mean of 107. Complete parts a through c below.**a. Test the null hypothesis that µ = 100 against the alternative hypothesis that µ > 100, using α = 0.05. Interpret the results of the test.**#### What is the value of the test statistic?\[ z = \square \text{ (Round to two decimal places as needed.)} \]This example illustrates hypothesis testing using a sample mean and known population standard deviation. The null hypothesis ($H_0$) states that the population mean ($µ$) is equal to 100, while the alternative hypothesis ($H_1$) states that the population mean ($µ$) is greater than 100. ### Step-by-Step Solution1. **State the Hypotheses:** - Null Hypothesis ($H_0$): $µ = 100$ - Alternative Hypothesis ($H_1$): $µ > 100$2. **Find the Test Statistic:** The test statistic is calculated using the formula for the z-score: \[ z = \frac{\overline{x} - µ}{\frac{σ}{\sqrt{n}}} \] Where: - $\overline{x}$ is the sample mean (107) - $µ$ is the population mean under the null hypothesis (100) - $σ$ is the population standard deviation (39) - $n$ is the sample size (100)3. **Calculate the Test Statistic:** \[ z = \frac{107 - 100}{\frac{39}{\sqrt{100}}} \] **Note:** Use this formula and given values to compute the z-score.4. **Compare the Test Statistic to the Critical Value:** For a one-tailed test with $α = 0.05$, the critical value (z-critical) is approximately 1.645.5. **Interpret the Results:** If the calculated z-value is greater than the z-critical value, we reject the null hypothesis.**Detailed Explanation:**- **Random Sample Size (n):** 100 observations- **Population Standard Deviation (σ

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A random sample of 100 observations from a population with standard deviation 39 yielded a sample mean of a. Test the null hypothesis thatu = 100 against the alternative hypothesis that u > 100, using a =0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.)

A random sample of 100 observations from a population with standard deviation 39 yielded a sample mean of a. Test the null hypothesis thatu = 100 against the alternative hypothesis that u > 100, using a =0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.)

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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