Newbie Here! Question on find number of test...

[redevo7]

This is a three part question where we are given a set of data samples.

coupon tip1 tip2
1 47 46
.
.
.
9 49 48
As quoted in problem:
"A Rockwell hardness-testing machine presses a tip into a test coupon and uses the depth of the resulting depression to indicate hardness. Nine coupons are tested, with both tips being tested on each coupon(who knows what a coupon is...) The data is shown in above table.



1. First set of questions asked to make any necessary assumptions to claim that both test(coupons) have the same readings. Check assumptions.

For this portion I just found the mean, and s² for each sample. Then I solved for s²p, then solved for t.

made my null hyp (u1-u2=0) and alt hyp (u1-u2 != 0)

Looked in table to find various values of t using a specific alpha and found any alpha worked.

2. Next question asked to determine that the difference in readings of the two tips is significantly different from zero.

I basically did the same as above and solved for z and compared to values of t alpha.

3. Question states "Suppose that 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 alpha =0.01, how many coupons(test) should have been used in the test? Test also different values of alpha"

Im confused as I have never heard the term "power of the test to be..."

I can already see how it would need to be solved but not sure what values I need to use and when to use the variables given i.e. alpha, mean dif of 1, and power of 0.9.

Can someone just point me in the right direction for what to do in the third question.

[redevo7]

If anyone could please help me find how to find number of test needed using given values of power, alpha and max mean difference. I just cant find the right formulation to solve it!