Question

Suppose that X1, X2,...,Xn and Y1, Y2,...,Yn are independent random samples from populations with means mu1 and mu2 and variances (sigma1)^2 and (sigma2)^2, respectively. SHow that Xbar - Ybar is a consistent estimator of mu1 - mu2

Answer 1

The difference between two sample means, Xbar - Ybar, is a consistent estimator of the difference between the population means, mu1 - mu2.

Step-by-step explanation:

In statistics, the difference between two sample means, Xbar - Ybar, is a consistent estimator of the difference between the population means, mu1 - mu2. This means that as the sample size increases, the estimated difference between the sample means will converge to the true difference between the population means.

Consistency is an important property of an estimator because it ensures that the estimated value becomes more accurate as more data is gathered. In this case, as the sample size increases, the estimate of mu1 - mu2 becomes more reliable.