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Define the rejection region as {y : ı – 2 < ci} where c is some real value. a) Calculate the Type I error rate. b) Propose a way to select c1. c) Find ei such that the Type I error rate is at most 0.05. d) Based on the observed data, test the hypothesis. What is your conclusion about the ability of the drug to reduce recovery time?

Define the rejection region as {y : ı – 2 < ci} where c is some real value. a) Calculate the Type I error rate. b) Propose a way to select c1. c) Find ei such that the Type I error rate is at most 0.05. d) Based on the observed data, test the hypothesis. What is your conclusion about the ability of the drug to reduce recovery time?

MATLAB: An Introduction with Applications
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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solve c and d only

Suppose we are developing a new drug that is supposed to improve the recovery time of an illness. We want to investigate if this is true. We conduct an experiment: we randomize twenty participants into two groups of size n = 10 each. In one group, we give the participants the drug. In the other group, we give them a placebo. We measure the recovery time of the participants in days. We observe the following data: • In the group given the drug, we observe recovery times (yı,..., Y10) = (15, 10, 13, 7,9, 8, 21,9, 14, 8), with ĝ1 = 11.4. • In the group given the placebo, we observe recovery times (yı1,..., Y20) = (15, 14, 12, 8, 14, 7, 16, 10, 15, 12) with j2 = 12.3. Assume that the data in each group follow Normal(µ1,0²) and Normal(42, o²) distributions respec- tively for the drug and placebo groups, o2 15. We want to test the following hypothesis: Ho : µ1 – 12 = 0 versus HA: µ1 – 42 < 0, using the test statistic T(Y) = Y1 – Ý2. a) Define the rejection region as {y : ĝı – 2 < c1} where ci is some real value. Calculate the Type I error rate. b) Propose a way to select c1. c) Find ci such that the Type I error rate is at most 0.05. d) Based on the observed data, test the hypothesis. What is your conclusion about the ability of the drug to reduce recovery time?
Transcribed Image Text:Suppose we are developing a new drug that is supposed to improve the recovery time of an illness. We want to investigate if this is true. We conduct an experiment: we randomize twenty participants into two groups of size n = 10 each. In one group, we give the participants the drug. In the other group, we give them a placebo. We measure the recovery time of the participants in days. We observe the following data: • In the group given the drug, we observe recovery times (yı,..., Y10) = (15, 10, 13, 7,9, 8, 21,9, 14, 8), with ĝ1 = 11.4. • In the group given the placebo, we observe recovery times (yı1,..., Y20) = (15, 14, 12, 8, 14, 7, 16, 10, 15, 12) with j2 = 12.3. Assume that the data in each group follow Normal(µ1,0²) and Normal(42, o²) distributions respec- tively for the drug and placebo groups, o2 15. We want to test the following hypothesis: Ho : µ1 – 12 = 0 versus HA: µ1 – 42 < 0, using the test statistic T(Y) = Y1 – Ý2. a) Define the rejection region as {y : ĝı – 2 < c1} where ci is some real value. Calculate the Type I error rate. b) Propose a way to select c1. c) Find ci such that the Type I error rate is at most 0.05. d) Based on the observed data, test the hypothesis. What is your conclusion about the ability of the drug to reduce recovery time?
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