Question

A company that makes robots has 12 new robots all designed for the same task. The company times all the robots as they complete their task. Then it modifies each robot’s mechanism. After the modificiation, it times the robots again as they complete their tasks. Assume that the first and second times for Robot i are (Xi , Yi) and that the pairs (X1, Y1),(X2, Y2), . . . ,(X12, Y12) are i.i.d. That means each pair is an independent copy of all other pairs. Remember that within each pair, the distribution of X and Y might be different. You can also assume that time is measured with enough precision that no two times come out exactly equal. Nine out of the 12 robots performed faster after modification. Come up with hypotheses that you can test to see whether the modifications did nothing or whether they made the robots faster. Perform the test at the 5% level and provide your conclusion. The test is called the sign test because it is based on the signs of the differences Di = Yi − Xi .

Answer 1