Question

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 hardness readings on average. Nine coupons are tested, with both tips being tested on each coupon. The data are given below (again, I apologize for not knowing the units): Coupon: 1 2 3 4 5 6 7 8 9 Tip 1 Depth: 47 42 43 40 42 41 45 45 49 Tip 2 Depth: 46 40 45 41 43 41 46 46 48 (a) What are the appropriate null and alternative hypotheses for addressing the question of interest? (b) Use JMP to perform the appropriate hypothesis test and draw a conclusion. Use  = 0.05. (As always, be sure to interpret the conclusion in the engineering context. (c) Find a 99% confidence interval based on the test data to characterize the difference between the two tips. (d) Suppose it was important to estimate the mean difference in depth between the two tips to within pm 0.5 units, with 99% confidence. How many coupons would need to be tested?

Name: 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 wh 45487
Uploaded: 2023-07-27T02:20:06-08:00
Duration: 2 min 36 s
Channel: Sri K
Description: 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 wh 45487

          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 hardness readings on average. Nine coupons are tested, with both tips being tested on each
coupon. The data are given below (again, I apologize for not knowing the units):
Coupon:        1    2    3   4     5   6   7    8   9
Tip 1 Depth: 47 42 43 40 42 41 45 45 49
Tip 2 Depth: 46 40 45 41 43 41 46 46 48
(a) What are the appropriate null and alternative hypotheses for addressing the question of interest?
(b) Use JMP to perform the appropriate hypothesis test and draw a conclusion. Use
 = 0.05. (As always, be
sure to interpret the conclusion in the engineering context.
(c) Find a 99% confidence interval based on the test data to characterize the difference between the two tips.
(d) Suppose it was important to estimate the mean difference in depth between the two tips to within pm  0.5 units,
with 99% confidence. How many coupons would need to be tested?

Added by Amy R.

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