A researcher wants to study the average lifetime of a certain brand of rechargeable batteries which has been advertised to be 950 hours. She suspects that the manufacturer is overstating the battery's capacity. So she select a random sample of 64 batteries from a normal population whose standard deviation she expects to be 200 hours. The sample mean was 920 hours Match the followng questions with the corresponding answers. Assume the level of significance to be 0.04.

The cut-off number of hours is

The p-value is

Based on her study, the researcher will

Supposed the true mean of the batteries is only 880 hours. What is the probability of Type I error?

Suppose the manufacutrer is really cheating the consumers. In reality, the batteries will last only 890 ours. What is the probability that the manufacturer will be caught?

choices below

Reject the Null 3.4% 902.65 74.2% 25.8% Not reject the Null Hypothesis. 906.25

14.7% 11.5% 7.63%