6.A certain type of calculator battery has a mean lifetime of µ =100 hours and a standard deviation σ= 10 hours. A company has developed a new battery and claims it has a different mean life. A random sample of 1000 batteries is tested and their sample mean lifetime 101 hours. Test to see if the null hypothesis is rejected at α = .05. a. What are your null and alternative hypotheses? b. What test is appropriate here? Why? c. What is your test statistic? d. What is your critical value? e. What is your final decision: do you reject the null or fail to reject the null?