Question: A type of lithium battery is being assessed for its length of life. The production manager selected a random sample of 10 batteries and recorded the following lifetimes in years: { 3.25, 4.0, 3.1, 3.7, 3.5, 4.2, 4.75, 2.3, 5.5, 3.7}. Answer the following assuming that the population is normal. (2 pts each)

a. What is the sample mean?

b. What is the sample standard deviation?

c. Explain how the sample mean is related to the population mean.

d. Assuming that you do not know the standard deviation of the population, construct a

90% confidence interval for \(\mu \) .

e. Assume that you do know that the standard deviation of the population is \(\sigma \) = 0.7; construct a 90% confidence interval for \(\sigma \) . (Show formula or calculator command)

f. Interpret the confidence interval in part e.