Let ? denote the life length, in hours, of a battery. Suppose ? is known to...

Let ? denote the life length, in hours, of a battery. Suppose ? is known to be normally distributed with standard deviation ? = 2.2 hours. A random sample of 16 batteries has an average life of ?̅ = 41.1 hours. We are interested in determining whether there is evidence to support the claim that mean battery life exceeds 40 hours. Using a level of significance of 0.05, answer the following questions.

a.) State the null and alternative hypothesis for the appropriate hypothesis test

b.)Identify the test statistic and critical region. State the conclusion of the test (i.e., should we reject or fail to reject).

c.) What is the ?-value for this test? Using this ?-value, what would be the conclusion of our test if the level of significance was changed to 0.025?

d.) What is the Type II error probability for the test if the true mean life is 41.496 hours? If the true mean life is 41.496 hours, what is the power of the test?

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orchestra answered 1 year ago

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