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d) Calculate the standard deviation of X- e) If we wish to create an 96% confidence interval for #x Hy then what is the z critical value used? f) Create an 96% confidence interval for Mx Hy. (L

d) Calculate the standard deviation of X- e) If we wish to create an 96% confidence interval for #x Hy then what is the z critical value used? f) Create an 96% confidence interval for Mx Hy. (L

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is 0x = 8.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is dy = 11.5. The true (unknown) mean 6AEQ for vaccine X recipients is μx, while the true (unknown) mean 6AEQ for vaccine Y recipients is y. 6AEQ measurements are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation Vaccine X 78 Vaccine Y 93 151 148 8.7 11.5 a) Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 78 vaccine X recipients. b)Calculate the variance of the random variable Y, which is the mean of the 6AEQ measurements of the 93 vaccine Y recipients. c) Calculate the variance of X - Y? d) Calculate the standard deviation of X - Y? e) If we wish to create an 96% confidence interval for x Hy then what is the z critical value used? f) Create an 96% confidence interval for Mx My. ( g) What is the length of your 96% confidence interval for μx Hy? h) If we used this data to test Ho: x - i) If we used this data to test Ho: x - y =0 against the alternative Ha: x y =0 against the alternative Ha: Mx j) If we used this data to test Ho: x - k) Copy your R script for the above into the text box here. Hy > 0 then what would the value of the calculated test statistic z have been? My >0 then what would the p value have been? y =0 against the alternative Ha: x-μy #0 then what would the p value have been?
Transcribed Image Text:Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is 0x = 8.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is dy = 11.5. The true (unknown) mean 6AEQ for vaccine X recipients is μx, while the true (unknown) mean 6AEQ for vaccine Y recipients is y. 6AEQ measurements are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation Vaccine X 78 Vaccine Y 93 151 148 8.7 11.5 a) Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 78 vaccine X recipients. b)Calculate the variance of the random variable Y, which is the mean of the 6AEQ measurements of the 93 vaccine Y recipients. c) Calculate the variance of X - Y? d) Calculate the standard deviation of X - Y? e) If we wish to create an 96% confidence interval for x Hy then what is the z critical value used? f) Create an 96% confidence interval for Mx My. ( g) What is the length of your 96% confidence interval for μx Hy? h) If we used this data to test Ho: x - i) If we used this data to test Ho: x - y =0 against the alternative Ha: x y =0 against the alternative Ha: Mx j) If we used this data to test Ho: x - k) Copy your R script for the above into the text box here. Hy > 0 then what would the value of the calculated test statistic z have been? My >0 then what would the p value have been? y =0 against the alternative Ha: x-μy #0 then what would the p value have been?
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