Chapter 8.8, Problem 92E

Solid copper produced by sintering (heating without melting) a powder under specified environmental conditions is then measured for porosity (the volume fraction due to voids) in a laboratory. A sample of n₁ = 4 independent porosity measurements have mean ${\bar{y}}_1$ = .22 and variance $s_1^2$ = .0010. A second laboratory repeats the same process on solid copper formed from an identical powder and gets n₂ = 5 independent porosity measurements with ${\bar{y}}_2$ = .17 and $s_2^2$ = .0020. Estimate the true difference between the population means (μ₁ − μ₂) for these two laboratories, with confidence coefficient .95.