A Rockwell hardness-testing machine presses a tip into a test coupon and uses the depth of the resulting depression to indicate hardness. Two different tips are being compared to determine whether they provide the same Rockwell C-scale hardness readings. Nine coupons are tested, with both tips being tested on each coupon. The data are as follows.

(a) State any assumptions necessary to test the claim that both tips produce the same Rockwell C-scale hardness readings.
Check those assumptions for which you have the data.

(b) Apply an appropriate statistical method to determine whether the data support the claim that the difference in Rockwell C-scale hardness readings of the two tips is significantly different from zero.

(c) Suppose that, if the two tips differ in mean hardness readings by as much as 1.0, we want the power of the test to be at least 0.9. For an 0.01, how many coupons should have been used in the test?

Coupon Tip 1 Tip 2 Coupon Tip 1 Tip 2 1 47 46 6 41 41 2 42 40 7 45 46 3 43 45 8 45 40 41 9 45 49 45 46 49 48 42 43