A battery manufacturer claims that the lifetime of its batteries average 20,000 hours. The standard deviation of lifetimes is known to be 4000 hours. You sample 100 batteries and will test the hypothesis that the mean lifetime is at least 20,000 hours versus the alternative that it is less.
a. If it is decided to reject H0 if the sample mean is less than 19,200, what is the level (α) of this test?
b. if, in fact, the true lifetime is 18,900 hours, what is the power of the test?
c. How many samples would you need to test if you wanted the power to be 90%?
The question belongs to Chemistry and it discusses about hypothesis testing of battery manufacturer who claims the batteries can last 20,000 hours.
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