Question

Suppose we take a random sample X1,…,X7 from a normal population with an unknown variance σ21 and unknown mean μ1. We also take another independent random sample Y1,…,Y6 from another normal population with an unknown variance σ22 and unknown mean μ2.

Construct a two-sided 90% confidence interval for σ21/σ22 if the observations are as follows: from the first population we observe

3.50,0.64,2.68,6.32,4.04,1.58,−0.45

and from the second population we observe

1.85,1.53,1.57,2.13,0.74,2.17

Answer 1

First we need to sample variances of both samples. Following table shows the descriptive statistics of both samples:

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