We wish to give a 95% confidence interval for μ 1 -μ 2 . Here, μ 1 denotes the mean value of the random variable Y 1 defined on Population 1, and μ 2 denotes the mean value of the random variable Y 2...

We wish to give a 95% confidence interval for μ₁-μ₂.  Here,  μ₁
denotes the mean value of the random variable Y₁
defined on Population 1, and μ₂
denotes the mean value of the random variable Y₂
defined on Population 2.  In order to develop the confidence interval we have obtained independent random samples of sizes 5 and 7 from Population 1 and Population 2, respectively.  For Population 1 we find a sample mean value of 12 with a sample standard deviation of 9, while the Population 2 sample has a mean value of 9 with a  sample standard deviation of 10.  Assume the Y₁
and Y₂
are normally distributed and have equal variances.  Find the pooled estimate of the common variance.