Suppose we take a random sample X1,…,X6 from a normal population with a known variance σ21=4...

Suppose we take a random sample X1,…,X6 from a normal population with a known variance σ21=4 and unknown mean μ1. We also collect an independent random sample Y1,…,Y5 from another normal population with a known variance σ22=1 and unknown mean μ2.

We use these samples to test the hypotheses

H0:μ1=μ2 vs. H1:μ1>μ2

with a critical region of the form {X¯−Y¯>k} for some constant k. Here Y¯ denotes the average of Yis just like X¯ denotes the average of Xis.

(1) - Determine k so that the type I error probability α of the test is equal to 0.0495.

(2) - For the value of k found in part (1), what is your conclusion in this test if you see the following data: from the first population we observe

2.19,−2.45,3.30,3.21,2.74,0.50

and from the second population we observe

0.57,1.14,2.91,1.19,0.58

Expert Solution

orchestra answered 2 years ago

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