Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is whichvaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 75recipients of vaccine X and 83 recipients of vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 129. Thevaccine Y recipients had a mean 6AEQ of y = 133. It is recognized that the true standard deviation of 6AEQ forvaccine X recipients is a = 9.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Yrecipients is σy = 10.7. The true (unknown) mean 6AEQ for vaccine X recipients is x, while the true (unknown)mean 6AEQ for vaccine Y recipients is My. 6AEQ measurements are known to be a normally distributed. Insummary:Type Sample Size Sample Mean Standard DeviationVaccine X 75129Vaccine Y 831339.710.7a)Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 75 vaccineX recipients.b)Calculate the variance of the random variable Y, which is the mean of the 6AEQ measurements of the 83 vaccineY recipients.c) Calculate the variance of X-Y?d) Calculate the standard deviation of X-Y?e) If we wish to create an 94% confidence interval for x - y then what is the z criticall vallue used?f)Create an 94% confidence interval for Mx Hy. (|g) What is the length of your 94% confidence interval for Mx Hy?h) If we used this data to test Ho: x - y =0 against the alternative H xHy <0 then what would the valueof the calculated test statistic z have been?i) If we used this data to test Ho: Mx - y =0 against the alternative Ha: Mx - My <0 then what would the p valuehave been?j)If we used this data to test Ho: x - y =0 against the alternative Hai Mx - My #0 then what would the p valuehave been?

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Answered: Suppose there are two different…

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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