Final answer:
The question involves calculating a 99% confidence interval for the mean battery life using a sample's statistics. The critical t-value is found using the t-distribution with 14 df for a 99% confidence interval, and the margin of error is calculated using that t-value, the sample standard deviation, and the square root of the sample size.
Step-by-step explanation:
The question asks about finding the critical value and margin of error for a 99% confidence interval for the mean lifetime of AA batteries, based on a sample. To begin with, the critical value (t*) is found using a t-distribution since the sample size is small (n=15) and the population standard deviation is unknown.
Finding the Critical Value
With a confidence level of 99% and a sample size of 15, the degrees of freedom (df) is 14 (df = n - 1). Using a t-distribution table or calculator, we can find the critical value for a two-tailed test at this confidence level and degrees of freedom.
Calculating the Margin of Error
The margin of error (ME) for a confidence interval is calculated using the formula ME = t* × (s/√n), where s is the sample standard deviation, n is the sample size, and t* is the critical value just found.