You have been given the task of designing a study concerning the lifetimes of five different types of electric motor. The initial question to be addressed is whether there are differences in mean lifetime among the five types. There are 20 motors, four of each type, available for testing. A maximum of five motors can be tested each day. The ambient temperature differs from day to day, and this can affect motor lifetime. a. Describe how you would choose the five motors to test each day. Would you use a completely randomized design? Would you use any randomization at all? b. If Xij represents the measured lifetime of a motor of type i tested on day j, express the test statistic for testing the null hypothesis of equal lifetimes in terms of the Xij.

Question

You have been given the task of designing a study concerning the lifetimes of five different types of electric motor. The initial question to be addressed is whether there are differences in mean lifetime among the five types. There are 20 motors, four of each type, available for testing. A maximum of five motors can be tested each day. The ambient temperature differs from day to day, and this can affect motor lifetime. a. Describe how you would choose the five motors to test each day. Would you use a completely randomized design? Would you use any randomization at all? b. If Xij   represents the measured lifetime of a motor of type i tested on day j, express the test statistic for testing the null hypothesis of equal lifetimes in terms of the Xij.

Leonard Stokes · Accepted Answer

(a) We can test at most 5 motors each day, while we have 20 motors in total and five different types of which there are 4 ench.  Note that we will then require 4 days to test all 20 motors at 5 motors per day.  We would then randomly select 1 of the 4 motors of each type to be used on the first day, then randomly select one of the remaining motors of exch type for the second day, etc.  This will result in a randomized block design where the blocks are the days and the treatments are the types. However, the design is not completely randomized as the randomization will only occur within each type.

Describe how you would choose the five motors to test each day. Would you use a completely randomized design? Would you use any randomization at all?

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