We want to test the relative efficacy of a new cholesterol lowering lrug A versus existing drug B. We randomize na subjects with high cholesterol to take reatment A and ng subjects to take treatment B. After a l-month followup, we measure holesterol levels in both groups. Suppose the data in the two groups are independent and A, YA,... YA N(µª,o²) and Y²,Y;",.…, ,YB N(µB,o²), where o? = 9 is known.
We want to test the relative efficacy of a new cholesterol lowering lrug A versus existing drug B. We randomize na subjects with high cholesterol to take reatment A and ng subjects to take treatment B. After a l-month followup, we measure holesterol levels in both groups. Suppose the data in the two groups are independent and A, YA,... YA N(µª,o²) and Y²,Y;",.…, ,YB N(µB,o²), where o? = 9 is known.
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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Kindly answer part 3 of this question.
Transcribed Image Text:We want to test the relative efficacy of a new cholesterol lowering
drug A versus existing drug B. We randomize nĄ subjects with high cholesterol to take
treatment A and ng subjects to take treatment B. After a l-month followup, we measure
cholesterol levels in both groups. Suppose the data in the two groups are independent and
YA,Y;ª,...,
YA N(µA, o²) and YB,YB,.., Y,B
iid
N(µB,0²), where o? = 9 is known.
Let Y4 and YB be the sample average cholesterol level in group A and B.
1. What is the distribution of the difference in sample means:  =Ÿª-ŸB? Hint: what
is the distribution of each group's sample average? What do we know about linear
combinations of normal RVs?
2. Let A = µA - µB be the true difference in cholesterol levels in populations treated with
Â-A
A versus B. What is the distribution of Z =
?
Vo2/na+o²/ng
3. Suppose YA = 20 and YB = 26 with na = nB = 36. Conduct an a = .05 significance
level test of Ho : A = 0 versus Ha : A # 0. Do you reject or fail to reject the null at
the .05 significance level? Be sure to find the distribution under the null, compute the
critical value, find the rejection region, and the compute the p-value.
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