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

Question

2. A battery pack used in a medical device needs to be recharged about every 5 hours. A random sample of 60 battery packs is selected and subjected to a life test. The average life of these batteries is 5.05 hours. Assume that battery life is normally distributed with standard deviation 0.3 hours. Is there evidence to support the claim that mean battery life is less than 4 hours? Use = 0.0 1. a. Write the appropriate hypothesis b. Use P-value approach to test the hypothesis. c. Use z-test to test the hypothesis d. Use confidence interval to test the hypothesis e. What is vour conclusion? f. If the true mean life is 4.5 hours, what is the type II error? g. If the true mean life is 4.5 hours, what is the minimum sample size needed to recognize it with 95% probability?

Explanation / Answer

a)
The hypothesis is
H0 : The mean battery life is not less than 4 hours
H1 : The mean battery life is less than 4 hours

b)

now we know that the z formula for difference in means is

z = (m1 -m2)/(sd/sqrt(n)) , where n is sample size

c)
putting the values as

z = (5.05-4)/(0.3/sqrt(60)) = 27.11

now we check the value from the ztable as
please note that this is a 1 tail test as we are interested in the less part

The P-Value is < 0.00001.

The result is significant at p < 0.01.

e)
as the p value is less than 0.01 , hence the result is signficant and we reject the null hypothesis in favor alternate hypothesis and conclude The mean battery life is less than 4 hours

Please ntoe that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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