BatCo (The Battery Company) produces your typical consumer battery. The company claims that their batteries last at least 100 hours, on average. Your experience with the BatCo battery has been somewhat different, so you decide to conduct a test to see if the companies claim is true. You believe that the mean life is actually less than the 100 hours BatCo claims. You decide to collect data on the average battery life (in hours) of a random sample and the information related to the hypothesis test is presented below. Hypothesized mean 100.0
Sample mean 98.5
Population standard deviation 3.5
Sample size 20
z-test statistic -1.93
p-value 0.0268
You want to prove your belief that the mean life is actually less than the 100 hours BatCo claims. In drawing your conclusion to your hypothesis test, you commit a Type II error. What does this mean?
A. You concluded that the average battery life was 100 or more hours, but in actuality, you are wrong--the company produces batteries that have an average life of less than 100 hours each.
B. You concluded that the average battery life was less than 100 hours, but in actuality, you are wrong--the company produces batteries that have an average life of 100 or more hours each.
C. You concluded that the average battery life was exactly 100 hours, but in actuality, you are wrong.
D. You set up your hypothesis test as a one-tailed test, but it is a two-tailed test.
E. You set up your hypothesis test as a two-tailed test, but it is a one-tailed test.
F. You defined your null and alternative hypotheses backwards.