Solve a and b 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 participantsinto two groups of size n = 10 each. In one group, we give the participants the drug. In the othergroup, we give them a placebo. We measure the recovery time of the participants in days. Weobserve 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, o215. 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 theability of the drug to reduce recovery time?

Name: Solve a and b Suppose we are developing a new drug that is supposed to
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Solve a and b 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 participantsinto two groups of size n = 10 each. In o