Question

Lifetimes (in years) of 50 car batteries of a certain brand are resulted in a mean of 3.12 years and a standard deviation of 1.02 years, respectively. What is the process for estimating the true mean lifetime of these batteries, and what statistical method is used to make this estimate?

Answer 1

To estimate the true mean lifetime of batteries, construct a confidence interval using the sample mean, standard deviation, and the z-distribution method, as the sample size is large.

Step-by-step explanation:

The process for estimating the true mean lifetime of these batteries involves constructing a confidence interval using the sample mean and standard deviation. As we have a sample size of 50, which is greater than 30, we can assume the sampling distribution of the mean is approximately normal due to the Central Limit Theorem. The statistical method used for this estimate is typically a t-distribution if the population standard deviation is unknown and the sample size is small; however, with a large sample size, we can use the z-distribution.

The formula for a confidence interval is:

CI = ± (z * (s/√n))

where CI is the confidence interval, z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size. By calculating this interval, we can estimate the range in which the true mean lifetime of the batteries is likely to fall.