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In: Statistics and Probability

A battery pack used in a medical device needs to be recharged about every 5 hours....

A battery pack used in a medical device needs to be recharged about every 5 hours. A random sample of 20 battery packs is selected and subjected to a life test. The average life of these batteries is 5.05 hours with standard deviation ?=0.3 hours. Assume that battery life is normally distributed. Is there evidence to support the claim that mean battery life is more than 5 hours? Use ?=0.01.

a. Use P-value approach to test the hypothesis.
b. Use t-test to test the hypothesis.
c. Use confidence interval to test the hypothesis

d. If the true mean life is 5.1 hours, what is the type II error?

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Expert Solution

A battery pack used in a medical device needs to be recharged about every 5 hours.

A random sample of 20 battery packs is selected and subjected to a life test.

The average life of these batteries is 5.05 hours with standard deviation ?=0.3 hours.

The battery life is normally distributed.

Here n=20,

=5.05, ?=0.3,

Here we have to test if the mean battery life is more than 5 hours i.e our hypothesis of chief interest are:

Null Hypothesis(H0):mean battery life ()=5 hours

vs

Alternative Hypothesis(H1):mean battery life > 5 hours.

orchestra answered 1 year ago
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