**Calculating Sample Size for a 95% Confidence Interval**To accurately estimate a population mean with a 95% confidence interval, it is critical to determine the required sample size that allows for the specified margin of error.**Given:**- Margin of error, \( E = 8.3 \) grams- Sample standard deviation, \( s = 62.1 \) grams**Objective:**Find the sample size needed to achieve this specified margin of error.**Solution:**The sample size formula for a confidence interval of the mean is:\[ n = \left( \frac{Z \cdot s}{E} \right)^2 \]Where:- \( n \) is the desired sample size.- \( Z \) is the Z-score corresponding to the 95% confidence level. For a 95% confidence level, \( Z \approx 1.96 \).- \( s \) is the sample standard deviation.- \( E \) is the margin of error.**Calculation:**Substitute the given values into the formula to find \( n \). After computing, remember to round up to the nearest whole number.**Output:**The required sample size is a rounded-up value based on the above calculation.**Instruction:**Make sure you perform this computation using appropriate tools or mathematical calculations to achieve the accurate sample size for precise data analysis in empirical research.

Answered: Assume that you want to construct a 95%…

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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Assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given. Margin of error, E=2.8 minutes; sample standard deviation, s=45.1 minutes The required sample size is ___?
You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 18 containers. Estimate the population standard deviation at a 98% level of confidence. 11.88 12.03 12.04 12.1 11.97 11.89 12.05 12.07 11.96 11.87 11.9 12 12.13 12.06 11.98 11.84 12.09 12.1 (Data checksum: 215.96) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper �2 critical values at 98% confidence:Lower: Upper: c) Report your confidence interval for �: ( , ) (check image)
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You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 17 containers. Estimate the population standard deviation at a 98% level of confidence. 11.94 11.93 12.04 11.99 12.06 11.92 11.98 12.11 11.83| 11.88 12.05 11.93 11.96 12.2 11.92 11.82 11.97 (Data checksum: 203.53) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper x critical values at 98% confidence: Lower: Upper: c) Report your confidence interval for o: (

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