Question

Suppose that Brooke is a manufacturing plant supervisor, and she is considering whether a new machine will pack items faster than their current machine. She selects independent simple random samples of packing times, in seconds, from both machines, summarized in the table. Population Population description Population mean Sample size Sample mean (s) Sample standard deviation (s) 1 New Machine ?1 (unknown) ?1=20 ?⎯⎯⎯1=45.231 ?1=0.797 2 Current Machine ?2 (unknown) ?2=18 ?⎯⎯⎯2=43.683 ?2=0.674 Brooke then formulates the following null and alternative hypotheses to reflect her belief that the new machine works faster than the current machine. ?0:?1?1:?1=?2>?2 Calculate the standard error estimate, SE, of the difference between the mean packing times of the two machines. Then calculate the value of the two-sample ? ‑statistic for this hypothesis test. Give your answer for the standard error rounded to five decimal places and your answer for the ? ‑statistic rounded to three decimal places. ?= SE =

Answer 1

The statistical software output for this problem is:

Hence,

t = 6.43

SE = 0.24090