A clockmaker is designing a decorative clock which will require only a small battery-powered motor and a flexible strip of metal for its operation. There are three types of alloys (labeled A, B, and C here) which seem to fit all requirements for the strip of metal, so the one to be used in the design will be the alloy which can be flexed for the longest period of time without breaking. A random sample of four strips of each type of alloy is obtained and all 12 strips are placed on a device which will continue to flex them until all break. They are observed periodically, and a record is kept, by alloy, of the order in which the strips break:
(First) ABAABABCBCCC (Last)
a. State the null and alternative hypotheses?
b. What is the critical value of the test statistic for an a = 0.05 test?
c. Compute the test statistic H and make the test of significance.
d. Use the procedure similar to Fisher's least significant difference to determine whether any alloy tends to outrank another with respect to length of time it can be flexed before breaking.