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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, Hx 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 y and Hy are unknown. It is recognized that the true standard deviations are a, = 19 for the 2020 measurements and e, = 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 - Hy- a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x - y ? c) Create a 95% confidence interval for y - Hy

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, Hx 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 y and Hy are unknown. It is recognized that the true standard deviations are a, = 19 for the 2020 measurements and e, = 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 - Hy- a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x - y ? c) Create a 95% confidence interval for y - 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, ux 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 Hy and Hy are unknown. It is recognized that the true standard deviations are ay = 19 for the 2020 measurements and oy = 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 Hx - Hy a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x- y ? c) Create a 95% confidence interval for My- Hy ? (C d) What is the length of the confidence interval in part c) ? e) 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? ) Copy your R script for the above into the text box here.
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, ux 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 Hy and Hy are unknown. It is recognized that the true standard deviations are ay = 19 for the 2020 measurements and oy = 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 Hx - Hy a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x- y ? c) Create a 95% confidence interval for My- Hy ? (C d) What is the length of the confidence interval in part c) ? e) 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? ) Copy your R script for the above into the text box here.
The weights of male students at a certain college are normally distributed with an unknown mean of u pounds and known standard deviation a = 10 pounds. We wish to create a confidence interval for u. We randomly select 16 male students and weigh each one. The sample gave a sample mean of x = 155 pounds, and a sample standard deviation s = 8 pounds. a)What is the critical value for a 95% confidence interval for u? b) Create a 95% confidence interval for u c) How long in pounds is the 95% confidence interval for u? d) How many observations would we need to guarantee that the 95% confidence interval above has a length of 5 pounds or less? e) Create a 95% prediction intervai for the weight of a single future randomly chosen male student at this college. f) Assuming a is not known, create a 95.0% confidence interval for u using this data. 9) What is the length of the confidence interval for part f? 9) Copy your R script for the above into the text box here.
Transcribed Image Text:The weights of male students at a certain college are normally distributed with an unknown mean of u pounds and known standard deviation a = 10 pounds. We wish to create a confidence interval for u. We randomly select 16 male students and weigh each one. The sample gave a sample mean of x = 155 pounds, and a sample standard deviation s = 8 pounds. a)What is the critical value for a 95% confidence interval for u? b) Create a 95% confidence interval for u c) How long in pounds is the 95% confidence interval for u? d) How many observations would we need to guarantee that the 95% confidence interval above has a length of 5 pounds or less? e) Create a 95% prediction intervai for the weight of a single future randomly chosen male student at this college. f) Assuming a is not known, create a 95.0% confidence interval for u using this data. 9) What is the length of the confidence interval for part f? 9) Copy your R script for the above into the text box here.
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