Acomputer company claims that the batteries in its laptops last 4 hours on average. a consumer report firm gathered a sample of 16 batteries and conducted tests on this claim. the sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. assume that the battery time distribution as normal.

a) test if the average battery time is shorter than 4 hours at a = 0.05.

b) construct a 95% confidence interval of the mean battery time.

c) if you were to test h0: µ =240 minutes vs. h1: µ ≠ 240 minutes, what would you conclude from your result in part (b)?

d) suppose that a further study establishes that, in fact, e population mean is 4 hours. did the test in part (c) make a correct decision? if not, what type of error did it make? 7. a computer company claims that the batteries in its laptops last 4 hours on average. a consumer report firm gathered a sample of 16 batteries and conducted tests on this claim. the sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. assume that the battery time distribution as normal.

a) test if the average battery time is shorter than 4 hours at a = 0.05.

b) construct a 95% confidence interval of the mean battery time.

c) if you were to test h0: µ =240 minutes vs. h1: µ ≠ 240 minutes, what would you conclude from your result in part (b)?

d) suppose that a further study establishes that, in fact, e population mean is 4 hours. did the test in part (c) make a correct decision? if not, what type of error did it make?