### Hypothesis Testing for Population MeanYou wish to test the following claim (Hypothesis \( H_a \)) at a significance level of \(\alpha = 0.005\):\[ H_0 : \mu = 89.6 \]\[ H_a : \mu < 89.6 \]You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n = 64 \) with a mean of \( M = 86.2 \) and a standard deviation of \( SD = 6.7 \).### Steps for Hypothesis Testing1. **Determine the critical value for the test:** What is the critical value for this test? (Report answer accurate to three decimal places.) \[ \text{critical value} = \_\_\_\_\_\_\_ \]2. **Calculate the test statistic:** What is the test statistic for this sample? (Report answer accurate to three decimal places.) \[ \text{test statistic} = \_\_\_\_\_\_\_ \]3. **Decision Rule:** Determine if the test statistic is in the critical region. - \(\circ\) in the critical region - \(\circ\) not in the critical region### Explanation- **Null Hypothesis (H0):** The population mean (\(\mu\)) is 89.6.- **Alternative Hypothesis (Ha):** The population mean (\(\mu\)) is less than 89.6.- **Sample Information:** - *Sample size (n):* 64 - *Sample mean (M):* 86.2 - *Sample standard deviation (SD):* 6.7- **Significance Level (\(\alpha\)):** 0.005To complete this test, you will need to determine the appropriate critical value for a one-tailed test with the given significance level, calculate the test statistic using the sample data, and then compare the test statistic to the critical value to make a decision on the null hypothesis.

The null and alternative hypotheses are:H0: μ = 89.6H1: μ < 89.6

Answered: You wish to test the following claim…

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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