MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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We want to test the relative efficacy of a new cholesterol lowering
drug A versus existing drug B. We randomize na subjects with high cholesterol to take
treatment A and nB subjects to take treatment B. After a 1-month followup, we measure
cholesterol levels in both groups. Suppose the data in the two groups are independent and
iid
YA, YA,..., YA
N(u4, o2) and YB,YB,.
YB id
N(µB, o²), 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: Â = ŸA-¥B? Hint: what
is the distribution of each group's sample average? What do we know about linear
combinations of normal RVs?
2. Let A = uA – µB be the true difference in cholesterol levels in populations treated with
A versus B. What is the distribution of Z =
Â-A
?
Vo? /na+o²/ng
3. Suppose YA
= 20 and YB
= 26 with na = nB = 36. Conduct an a = .05 significance
level test of Họ : 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.
Construct a 95% interval estimator for A in Problem 4.1-4.3 by
inverting the test you found in that problem. Derive the interval estimator in general terms,
then substitute the data values from part 4.3 to compute an interval estimate. Interpret the
confidence interval estimate.
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Transcribed Image Text:We want to test the relative efficacy of a new cholesterol lowering drug A versus existing drug B. We randomize na subjects with high cholesterol to take treatment A and nB subjects to take treatment B. After a 1-month followup, we measure cholesterol levels in both groups. Suppose the data in the two groups are independent and iid YA, YA,..., YA N(u4, o2) and YB,YB,. YB id N(µB, o²), 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: Â = ŸA-¥B? Hint: what is the distribution of each group's sample average? What do we know about linear combinations of normal RVs? 2. Let A = uA – µB be the true difference in cholesterol levels in populations treated with A versus B. What is the distribution of Z = Â-A ? Vo? /na+o²/ng 3. Suppose YA = 20 and YB = 26 with na = nB = 36. Conduct an a = .05 significance level test of Họ : 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. Construct a 95% interval estimator for A in Problem 4.1-4.3 by inverting the test you found in that problem. Derive the interval estimator in general terms, then substitute the data values from part 4.3 to compute an interval estimate. Interpret the confidence interval estimate.
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