**Problem 27: Confidence Interval for Lemon Quality**Bob draws a simple random sample from an extremely large population of lemons. The sample size is \( n = 700 \), where 250 lemons are found to be good and 450 lemons are found to be bad. Determine the 95% confidence interval for the population proportion \( p \) of good lemons.**Choices:**A. (0.30165, 0.37264) B. (0.31165, 0.38264) C. (0.32165, 0.39264) D. (0.33165, 0.40264) **Solution Approach:**To calculate the confidence interval, use the formula for the confidence interval for a population proportion:\[\hat{p} = \frac{\text{Number of good lemons}}{\text{Total sample size}} = \frac{250}{700} \]Next, find the standard deviation for the sample proportion:\[\sigma_{\hat{p}} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]Finally, use the z-score for a 95% confidence level (approximately 1.96) to find the margin of error and construct the confidence interval:\[CI = \hat{p} \pm z \times \sigma_{\hat{p}}\]Evaluate which of the given options corresponds to the calculated interval.

Here we need to find confidence interval for population proportion p of good lemons.

Answered: 27. Bob-draws a simple random sample…

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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