# Thread: Testing for differences between populations

1. ## Testing for differences between populations

Could someone please tell me if there is something wrong?

Q. An experiment is performed to compare the effectiveness of two treatments which are designed to improve the resistance of a certain metal against corrosion. Eight sheets of the metal are each divided into two equal-sized pieces which are weighed. One piece from each pair, chosen at random, is assigned to treatment 1 and the second to treatment 2. After treatment the pieces are immersed in acid for a fixed time, and then are removed and weighed. The loss of mass, in grams, for each piece, is given in the following table.

treatment1 3.1 2.8 2.9 3.2 3.3 3.2 2.6 3.0
treatment2 3.1 3.2 3.4 3.5 2.8 3.5 2.7 3.2

Stating suitable assumptions, calculate a symmetric 95% confidence interval for the mean difference in losses between the two treatments. Given the end points correct to two decimal places.

I see this as a paired t-test so the confidence interval would be
[d-bar - t x Sd x (1/n)^1/2 , d-bar + t x Sd x (1/n)^1/2]

[0.1625 - 2.365 X0.31139089x(1/8)^(1/2), 0.1625 - 2.365 X0.31139089x(1/8)^(1/2)]
[-.10,0.42]

Book gives [0.10,0.42]. Is it standard to give differences in +ve answers? But that would imply that at 95% it doesnt pass through 0 differece.

Thanks.

2. Most likely it's a typo in your book.
They just left out the negative sign.