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 78recipients 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 forvaccine 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 DeviationVaccine X 78Vaccine Y 931511488.711.5a) 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: xy =0 against the alternative Ha: Mxj) 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?

Given Information: Vaccine X: Sample size nx=78 Sample mean x¯=151 Population standard deviation…

Answered: uppose there vid, vaccine X vaccine An…

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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Researchers are interested in the effect of pet companionship on depression in elderly adults. They randomly select 25 participants from the target population and record their depression scores before and after spending a month with a dog (a higher score indicates a higher level of depression). The researchers then compute the difference scores for each participant (difference after before). The mean of differences is - 1 and the standard deviation of differences is 2. Can the researchers conclude that there is an effect of pet companionship on depression in elderly adults? Conduct the appropriate statistical test (two-tailed) with a = .05. Based on the information provided above, which statistical test seems most appropriate? one sample t test O z test independent samples t test O dependent samples t test
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Your research group has been hired to determine if college men and women drink different amounts of soft drinks at Illinois State University. After a careful study, your group has determined that males drink an average of 12 sodas per week with a standard deviation of 3.5 whereas female students drink an average of 9 soft drinks per week with a standard deviation of 2 sodas. The sample size of males is 200 and the sample size of females is 200. Based on this information, your group calculates the z-score to be: [____].

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