Probability 9.

(b) An experiment was conducted to determine whether two different brands of batteries have similar lifetimes. A random sample of batteries was obtained from each brand and their lifetimes were measured. The measurements are summarised in the table below. Sample size Sample mean Sample standard deviation Battery brand 1 37 22.15 2.00 Battery brand 2 36 23.15 2.10 i. Use an appropriate hypothesis test to determine whether there is a difference between the mean battery lifetimes of the two brands. State clearly the hypotheses, the test statistic and its distribution under the null hypothesis, and carry out the test at two appropriate significance levels. Comment on your findings. ii. State clearly any assumptions you made in (b) part i. iii. Repeat the procedure in (b) part i. to determine whether the mean battery lifetime of brand 1 is shorter than that of brand 2