You measure the lifetime of a randomsample of 25 batteries of a certain brand. T

Question

You measure the lifetime of a randomsample of 25 batteries of a certain brand. The sample mean is Xbar= 980 hours. Suppose that the lifetimes for batteries of this brandfollow a normal distribution, with unknown mean µand standard deviation = 80 hours.

    (a) Calculate a 99%confidence interval for the mean lifetime in thepopulation of all batteries of this brand.

         (b) What is the margin of errorfor the 99% confidence interval?

How large a sample would enable you to estimatethe mean lifetime of batteries of a certain brand. within a marginof error of ±20 hours? The standard deviation of thelifetime of this brand of tires is = 80hours

(a) Calculate the sample sizewith 99% confidence. Treat these batteries as anSRS.

(b) Now, calculate the samplesize with 90% confidence.

(c) Compare the results in (a) and (b).

Explanation / Answer

(a) Calculate a 99% confidence intervalfor the mean lifetime in the population of allbatteries of this brand.

=0.01, |Z(0.005)|=2.58 (check normal table)

The 99% CI is

xbar ± Z*/n

--> 980 ± 2.58*80/sqrt(25)

--> ( 938.72, 1021.28)

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