Discuss the below:
The manufacturer of batteries used in small electric appliances wants to establish the average life of a battery. A random sample of 12 batteries yields a sample mean of 34.2 hours, and a sample standard deviation of 5.9 hours. Give a 95% confidence interval for the average life of a battery. Assume the underlying distribution is normal.
Q: How many test runs (i.e. minimum sample size) of an automobile are required for determining it's average miles-per-gallon rating on the highway to within 2 miles per gallon with 95% confidence, if a good guess is that the variance of the population of miles per gallon is about 100?