The lifetime of a certain brand of battery is known to have a standard deviation of 16 hours. Suppose that a random sample of 70 such batteries has a mean lifetime of 41 hours. Based on this sample, find a 90% confidence interval for the true mean lifetime of all batteries of this brand. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
A. What is the lower limit of the 90% confidence interval?
B. What is the upper limit of the 90% confidence interval?
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Solution. Denote by xbar the sample mean lifetime of all batteries of this brand. From the given information, we know that
This solution shows step-by-step calculations to determine the upper and lower limit of a 90% confidence interval.