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What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y ? Create a 95% confidence interval for u, - Hy

What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y ? Create a 95% confidence interval for u, - Hy

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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Has the number of shoppers who wear masks changed from 2020 to 2021? There are arguments for and against this question. The mean number of masks, u, used by a shopper in Metropolis in 2020 will be compared to the mean number of masks, Hy used by a shopper in Metropolis in 2021. The true values of u, and u, are unknown. It is recognized that the true standard deviations are o, = 19 for the 2020 measurements and o, = 24 for the 2021 measurements. We take a random sample of m = 255 shoppers in 2020 and a random sample of n = 200 shoppers in 2021. The mean number of masks were x= 97 for 2020 and y= 85 for 2021. Assuming independence between the years and assuming masks used by shoppers are normally distributed we would like to estimate x - Hy. What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y? Create a 95% confidence interval for uy - Hy ? ) What is the length of the confidence interval in part c) ? If we let n stay at 200 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 7 or less?
Transcribed Image Text:Has the number of shoppers who wear masks changed from 2020 to 2021? There are arguments for and against this question. The mean number of masks, u, used by a shopper in Metropolis in 2020 will be compared to the mean number of masks, Hy used by a shopper in Metropolis in 2021. The true values of u, and u, are unknown. It is recognized that the true standard deviations are o, = 19 for the 2020 measurements and o, = 24 for the 2021 measurements. We take a random sample of m = 255 shoppers in 2020 and a random sample of n = 200 shoppers in 2021. The mean number of masks were x= 97 for 2020 and y= 85 for 2021. Assuming independence between the years and assuming masks used by shoppers are normally distributed we would like to estimate x - Hy. What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y? Create a 95% confidence interval for uy - Hy ? ) What is the length of the confidence interval in part c) ? If we let n stay at 200 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 7 or less?
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