Q1) As a chemist working for a battery manufacturer, you are given the problem of developing an improved battery for a calculator that will last "significantly longer" than the current battery. You know that the measures of the current battery's lifetime in the calculator are normally distributed with $\mu = 100.3$ min and $\sigma = 6.25$ min. You develop an improved battery that theoretically should last longer, and from preliminary tests you decide that you can assume that its lifetime measures are also normally distributed with $\sigma = 6.25$ min. To do a test of $H_0: \mu = 100.3$ min, you take a sample of n=15 lifetimes of the improved battery in the calculator and find that $\bar{X} = 105.6$ min (a) Do a two-tailed test of the $H_0$ using $\alpha = 0.01$ (b) Find P-values Q2) You repeat the battery study in (Q1), (n=20, $\bar{X} = 105$ min, $\sigma = 6.25$ min) (a) Do a right-tailed test of $H_0: \mu = 100.3$ min at $\alpha = 0.05$ (b) Find P-values (c) Find the 90% C.I for $\mu$ (d) Find the 95% C.I for $\mu$ (e) Find the 99% C.I for $\mu$
