A manufacturer of car batteries claims that his batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries have lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence interval for σ² = and decide if the manufacturer's claim that σ² = 1 is valid. Assume the population of battery lives to be approximately normally distributed.