### Statistical Hypothesis Testing#### Problem Statement**6. Suppose you are testing:**\[ H_0: p = 0.8 \quad \text{versus} \quad H_1: p < 0.8, \]where \( n = 25 \). From your data, you calculate your test statistic value as \( +1.2 \).**Tasks:**(a) Should you use \( z \) or \( t \) when finding a p-value for this scenario?(b) Calculate the p-value for this scenario.(c) Using a significance level of 0.062, what decision should you make (Reject \( H_0 \) or Do Not Reject \( H_0 \))?---#### Detailed Explanation- **Test Statistic**: We have a test statistic value of \( +1.2 \).- **Sample Size \( n \)**: 25. - **Null Hypothesis \( H_0 \)**: Population proportion \( p = 0.8 \).- **Alternative Hypothesis \( H_1 \)**: Population proportion \( p < 0.8 \).- **Significance Level**: 0.062.---#### Solution Approach1. **Choosing Between \( z \) and \( t \):** - Since we are dealing with proportions and assuming a normal approximation is valid due to reasonable sample size, use the \( z \)-test.2. **P-value Calculation:** - Use the standard normal distribution to find the p-value corresponding to a test statistic of \( +1.2 \). Since this is a one-tailed test (because \( H_1: p < 0.8 \)), the p-value is the probability that \( Z > 1.2 \).3. **Decision Making:** - Compare the p-value with the significance level (0.062). - If the p-value is less than the significance level, reject \( H_0 \). - Otherwise, do not reject \( H_0 \).Use statistical calculators or tables to determine exact values as needed.

Answered: 6. Suppose you are testing Ho: p= 0.8…

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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