A manufacturer of car batteries claims that the 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.

A) Interval for σ² is;

0.29 < σ² < 6.74

B) The manufacturer's claim that σ² = 1 is valid.

Step-by-step explanation:

A) I have attached the explanation

B) Due to the fact that the 95% confidence interval level for σ² is from 0.29 to 6.74 and that 1 falls within that range, we can say that the manufacturer's claim that σ² = 1 is valid.

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative