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Zobt of 3.33 falls in the Critical Region (Rejection Region) with Zerit of| Therefore, the result indicates a significant difference between the population mean and the Can we reject Ho at a =.01? (a = .01). %3D sample mean of IQ test scores. The pills do work. 99% Level of Confidence Fail to Reject Reject Reject 0.5% 0.5% 3.33 Zcrit = -2.576 Z crit = +2.576 %3! Zobt

Zobt of 3.33 falls in the Critical Region (Rejection Region) with Zerit of| Therefore, the result indicates a significant difference between the population mean and the Can we reject Ho at a =.01? (a = .01). %3D sample mean of IQ test scores. The pills do work. 99% Level of Confidence Fail to Reject Reject Reject 0.5% 0.5% 3.33 Zcrit = -2.576 Z crit = +2.576 %3! Zobt

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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**Title: Understanding Hypothesis Testing: Two-Tailed Z Test** **Can we reject H₀ at α = .01?** The observed Z-score (\( Z_{\text{obt}} \)) of 3.33 falls within the Critical Region (Rejection Region) with \( Z_{\text{crit}} \) of ±2.576 (α = .01). This indicates a significant difference between the population mean and the sample mean of IQ test scores. Thus, the hypothesis that the pills do work is supported. **Diagram Explanation:** The diagram shown is a standard normal distribution curve illustrating a two-tailed Z test at a significance level (α) of 0.01. Here's a detailed explanation: - **Middle Section (Fail to Reject Region):** Represents 99% Level of Confidence where we do not reject the null hypothesis. - **Critical Regions:** - **Left Tail (Reject Region):** Contains 0.5% of the distribution; we reject H₀ for values of \( Z \) less than -2.576. - **Right Tail (Reject Region):** Contains 0.5% of the distribution; we reject H₀ for values of \( Z \) greater than +2.576. - **Observed Value:** - \( Z_{\text{obt}} = 3.33 \), which is in the right Rejection Region, leading to the rejection of H₀. **Let's Practice Two-Tailed Z Test** *Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw corn starch will have a negative or positive effect on blood glucose levels. A sample of 30 patients who have tried the raw corn starch diet have a mean of...* This practice section sets up a scenario where you can apply a two-tailed Z test to determine the effect of a dietary change, using the concepts highlighted above.
Transcribed Image Text:**Title: Understanding Hypothesis Testing: Two-Tailed Z Test** **Can we reject H₀ at α = .01?** The observed Z-score (\( Z_{\text{obt}} \)) of 3.33 falls within the Critical Region (Rejection Region) with \( Z_{\text{crit}} \) of ±2.576 (α = .01). This indicates a significant difference between the population mean and the sample mean of IQ test scores. Thus, the hypothesis that the pills do work is supported. **Diagram Explanation:** The diagram shown is a standard normal distribution curve illustrating a two-tailed Z test at a significance level (α) of 0.01. Here's a detailed explanation: - **Middle Section (Fail to Reject Region):** Represents 99% Level of Confidence where we do not reject the null hypothesis. - **Critical Regions:** - **Left Tail (Reject Region):** Contains 0.5% of the distribution; we reject H₀ for values of \( Z \) less than -2.576. - **Right Tail (Reject Region):** Contains 0.5% of the distribution; we reject H₀ for values of \( Z \) greater than +2.576. - **Observed Value:** - \( Z_{\text{obt}} = 3.33 \), which is in the right Rejection Region, leading to the rejection of H₀. **Let's Practice Two-Tailed Z Test** *Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw corn starch will have a negative or positive effect on blood glucose levels. A sample of 30 patients who have tried the raw corn starch diet have a mean of...* This practice section sets up a scenario where you can apply a two-tailed Z test to determine the effect of a dietary change, using the concepts highlighted above.
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