Question

An article reports that the average initial rate of absorption in g/min-cm) for a sample of five clay bricks with fine glass particles added was 1299.8 with a standard deviation of 329.8, and the average for another sample of fifteen bricks without glass particles added was 4500.8 with a standard deviation of 2716. Let XuX represent the population mean without glass particles and let uyuy represent the population mean with glass particles. Find a 98% confidence interval for the difference X-YuX-Y. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

Answer 1

Standard Error
s(M1 - M2) = √((s12/n1) + (s22/n2)) = √((329.8^2/5) + (271.6^2/15)) = 163.31

Confidence Interval
μ1 - μ2 = (M1 - M2) ± ts(M1 - M2) = -3201 ± (3.156 * 163.31) = -3201 ± 515.406

μ1 - μ2 = (M1 - M2) = -3201, 95% CI [−3716.382<μ1​−μ2​<−2685.618.].

You can be 95% confident that the difference between your two population means (μ1 - μ2) lies between −3716.382<μ1​−μ2​<−2685.618.