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est the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.88 versus H₁: p=0.88 n=500, x=430, α = 0.05 ... - OB. No, because (1) Now find p. p= 0.86 (Type an integer or a decimal. Do not round.) Find the test statistic Zo- Zo= (Round to two decimal places as needed.)

est the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.88 versus H₁: p=0.88 n=500, x=430, α = 0.05 ... - OB. No, because (1) Now find p. p= 0.86 (Type an integer or a decimal. Do not round.) Find the test statistic Zo- Zo= (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
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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### Testing the Hypothesis using the P-value Approach Be sure to verify the requirements of the test. **Hypotheses:** \( H_0 \): \( p = 0.88 \) versus \( H_1 \): \( p \ne 0.88 \) **Given:** - Sample size: \( n = 500 \) - Number of successes: \( x = 430 \) - Significance level: \( \alpha = 0.05 \) --- **Step-by-Step Solution:** 1. **Calculate \(\hat{p}\)** (sample proportion): \[ \hat{p} = \frac{x}{n} = \frac{430}{500} = 0.86 \] (Type as an integer or a decimal. Do not round.) 2. **Find the test statistic \( z_0 \)**: \[ z_0 = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] \[ z_0 = \text{(Round to two decimal places as needed.)} \] --- **Support Resources:** - Help me solve this - View an example - Get more help *Note: Be attentive to the rounding instructions and usage of decimal points as specified in the steps.* --- Understanding the hypothesis testing approach and using the P-value method effectively helps in making informed decisions in statistics. The result provides evidence on whether to reject the null hypothesis based on the given sample data and the significance level. **Educational Insight:** This example assists in comprehending the steps involved in hypothesis testing, emphasizing the importance of verifying requirements, calculating sample proportions, and finding test statistics accurately. --- *Interactive Tools:* - Calculator for \(\hat{p}\) and \( z_0 \) - Tutorials on hypothesis testing - Additional exercises *Engage with practical examples for better learning outcomes!*
Transcribed Image Text:### Testing the Hypothesis using the P-value Approach Be sure to verify the requirements of the test. **Hypotheses:** \( H_0 \): \( p = 0.88 \) versus \( H_1 \): \( p \ne 0.88 \) **Given:** - Sample size: \( n = 500 \) - Number of successes: \( x = 430 \) - Significance level: \( \alpha = 0.05 \) --- **Step-by-Step Solution:** 1. **Calculate \(\hat{p}\)** (sample proportion): \[ \hat{p} = \frac{x}{n} = \frac{430}{500} = 0.86 \] (Type as an integer or a decimal. Do not round.) 2. **Find the test statistic \( z_0 \)**: \[ z_0 = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] \[ z_0 = \text{(Round to two decimal places as needed.)} \] --- **Support Resources:** - Help me solve this - View an example - Get more help *Note: Be attentive to the rounding instructions and usage of decimal points as specified in the steps.* --- Understanding the hypothesis testing approach and using the P-value method effectively helps in making informed decisions in statistics. The result provides evidence on whether to reject the null hypothesis based on the given sample data and the significance level. **Educational Insight:** This example assists in comprehending the steps involved in hypothesis testing, emphasizing the importance of verifying requirements, calculating sample proportions, and finding test statistics accurately. --- *Interactive Tools:* - Calculator for \(\hat{p}\) and \( z_0 \) - Tutorials on hypothesis testing - Additional exercises *Engage with practical examples for better learning outcomes!*
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