Question

A company claims that its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don't last that long, so an independent testing agency is engaged to test them. The population standard deviation is known to be 10 hours. For the 25 batteries they tested, the mean lifetime was 96 hours.

If the true population mean is 100 hours, you have made a
Type I Error      Type II error   Correct decision
If the level of significance had been .01, would your answer to part b change?
Yes      No

Answer 1

Ho: = 100

Ha: < 100 [Left Tailed Test]

Test statistic

z = -2

p - Value = P(z < -2) = 0.0228

Since p - value is less than 0.05, we reject Ho and conclude that the mean is less than 100.

If the true population mean is 100 hours, you have made a

Type I error because we rejected a true null hypothesis.

If the level of significance had been .01, would your answer to part b change?

Yes