CHARACTERIZING "FAST-ACTING" RAT POISON

The scientists at the ACME rat poison laboratories, who have been working non-stop to develop a new "fast-acting" formulation that will break the "thousand-second" barrier, appear to be on the verge of a breakthrough. Their target is a product that will kill rats within 1000 secs, on average, with a standard deviation of 125 secs. Experimental tests conducted in an affliated toxicology laboratory in which pel- lets were made with a newly developed formulation and administered to 64 rats (selected at random from an essentially identical popula- tion). The results showed an average "acting time," x¯ = 1028 secs. The ACME scientists, anxious to declare a breakthrough, were preparing to approach management immediately to argue that the observed ex- cess 28 secs, when compared to the stipulated standard deviation of 125 seconds, is "small and insigni?cant." The group statistician, in an attempt to present an objective, statistically-sound argument, recom- mended instead that a hypothesis test should ?rst be carried out to rule out the possibility that the mean "acting time" is still greater than 1000 secs. Assuming that the "acting time" measurements are normally distributed, carry out an appropriate hypothesis test and, at the signif- icance level of α = 0.05, make an informed recommendation regarding the tested rat poison's "acting time."