Question

Construct a​ 95% confidence interval for mu 1minusmu 2. Two samples are randomly selected from each population. The sample statistics are given below. n 1 equals ​50, n 2 equals ​60, x overbar 1 equals​25, x overbar 2 equals​23, sigma 1 equals​1.5, sigma 2 equals1.9

Answer 1

Before we go on to solve the problem let us know a bit about confidence interval.

Confidence Interval

Suppose we want to find a confidence interval for θ.

If a very large number of samples, each of size n are taken from the population and if for each sample the confidence interval is determined then in about 100(1-α)% of the cases the interval will include θ, where α is the level of significance.

Coming back to our problem

Here we need to find a 95% confidence interval for μ₁-μ₂.

A 95% confidence interval for μ₁-μ₂ is given by,

Given,

[From Biometrika Tables]

Lower Limit

Upper Limit

Hence a 95% confidence interval for μ₁-μ₂ is given by (1.3644,2.6356)