Round to 3 decimal points

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 68 recipients of vaccine X and 80 recipients of vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 129. The vaccine Y recipients had a mean 6AEQ of y = 133. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is Ox = 9.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is Oy = 10.7. The true (unknown) mean 6AEQ for vaccine X recipients is ux , while the true (unknown) mean 6AEQ for vaccine Y recipients is My . 6AEQ measurements are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation Vaccine X 68 129 Vaccine Y 80 133' 10.7 a) Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 68 vaccine X recipients. b) Calculate the variance of the random variable Y, which is the mean of the 6AEQ measurements of the 80 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 - My then what is the z critical value used? f)Create an 96% confidence interval for Ax - My . 9) What is the length of your 96% confidence interval for MX - My ? h) If we used this data to test Ho: My - My =0 against the alternative Ha: My - My