**Constructing a 99% Confidence Interval for a Population Proportion**To construct the 99% confidence interval estimate for the population proportion \( p \), we start with the given data:- Sample size (\( n \)) = 300- Number of successes (\( x \)) = 221Next, we follow these steps:1. Calculate the sample proportion (\( \hat{p} \)). \[ \hat{p} = \frac{x}{n} = \frac{221}{300} \]2. Determine the standard error (SE) of the sample proportion. \[ SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]3. Identify the z-score corresponding to the 99% confidence level. For a 99% confidence interval, this z-score is typically 2.576.4. Calculate the margin of error (ME). \[ ME = z \times SE \]5. Finally, construct the confidence interval. \[ \hat{p} - ME < p < \hat{p} + ME \]The blank areas in the image indicate where the calculated lower and upper bounds of the confidence interval will be input. These calculations provide the range within which the true population proportion \( p \) lies with 99% confidence.

Obtain the 99% confidence interval estimate of the population proportion. The 99% confidence interval estimate of the population proportion is obtained below: Obtain the area of probability in the right tail. Use EXCEL Procedure for finding the critical value of z. Follow the instruction to obtain the critical value of z: Open EXCEL Go to Formula bar. In formula bar enter the function as“=NORMINV” Enter the probability as 0.995 Enter the mean as 0 and the Standard deviation as 1. Click enter EXCEL output: From the EXCEL output, the critical value of z at the 99% confidence level is 2.576.The value of sample proportion is, The 99% confidence interval estimate of the population proportion lies between 0.6712<p<0.8022.

Answered: Construct the 99% confidence interval…

Math

Statistics

Construct the 99% confidence interval estimate of the population proportion p if the sample size is n = 300 and the number of successes in the sample is = 221. < p<

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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