## Clinical Trial for Increasing Probability of Conceiving a Girl: An AnalysisA clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 656 babies were born, and 328 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?### Constructing the Confidence IntervalThe problem requires the construction of a 99% confidence interval for the proportion \( p \) of girls born. The interval will be of the form:\[ \text{Confidence Interval} = \left( \hat{p} - E, \hat{p} + E \right) \]Where:- \( \hat{p} \) is the sample proportion (\( \hat{p} = \frac{\text{number of girls}}{\text{total number of babies}} \)).- \( E \) is the margin of error calculated as \( E = Z \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \), where \( Z \) is the z-score corresponding to the confidence level and \( n \) is the total number of babies.### Data Provided:- **Total number of babies born (n)**: 656- **Number of girls (x)**: 328### Calculation1. **Sample Proportion (\( \hat{p} \))**: \[ \hat{p} = \frac{328}{656} = 0.5 \]2. **Z-Score for a 99% Confidence Level**: The Z-score corresponding to a 99% confidence interval is approximately 2.576.3. **Margin of Error (E)**: \[ E = 2.576 \cdot \sqrt{\frac{0.5 \cdot (1 - 0.5)}{656}} = 2.576 \cdot \sqrt{\frac{0.25}{656}} \approx 2.576 \cdot 0.0196 = 0.0505 \]4. **Confidence Interval**: \[ \text{Confidence Interval} = (0.5 - 0.0505, 0.5 + 0.0505) = (

In statistical inference, there are two types of estimation, Point estimation and Interval…

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 656 babies were born, and 328 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 656 babies were born, and 328 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

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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