Question

The lifetime of a certain brand of battery is known to have a standard deviation of 16 hours. Suppose that a random sample of 50 such batteries has a mean lifetime of 37.6 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. ( If necessary, consult a list of formulas.)

What is the lower limit of the 90% confidence interval?

What is the upper limit of the 90% confidence interval?

Answer 1

Given that the life-time of a certain brand of battery is known to have a standard deviation of = 16 hours. Suppose that a random sample of n = 50 such batteries has a mean lifetime of =37.6 hours.

For the above-given details, the confidence interval is calculated as:

where Zc is critical Z score for normal distribution which is calculated using excel formula for normal distribution with the help of confidence level, the formula used is =NORM.S.INV(0.95) which results in Zc = 1.645

Now the confidence interval is calculated as:

So, the lower limit is 33.9 and the Upper limit is 41.3