3. An article reports on a study using high temperature strain gages to measure the total strain amplitude ('m/2) of different types of cast iron

3. An article reports on a study using high temperature strain gages to measure the total strain amplitude

('εm/2) of different types of cast iron for use in disc brakes.6 The results for spheroidal graphite (SG) and compacted graphite (CG), multiplied by 10,000, are given below:

Are the total amplitude strain properties of the different types of cast iron significantly different at level of significance α = 0.05?

(a) State the appropriate null and alternative hypotheses, conduct the rank-sum procedure in (9.3.5), and compute the p-value. (You may use theRcommands given in Example 9.3-1 instead of hand calculations.)

(b) Use R commands to (i) carry out the test on the basis of the exact p-value, and (ii) construct a 95% CI for the median of the difference between a measurement from SG and one from CG cast iron.

SG 105 77 52 27 22 17 12 14 65 CG 90 50 30 20 14 10 60 24 76