8. The Acme Company has developed a new battery. The engineer in charge claims that the new battery will operate longer than the old battery. To test the claim, the company selects a simple random sample of 35 new batteries and 45 old batteries. The old batteries run continuously for 168 minutes with a standard deviation of 10 minutes. The new batteries run for 173 minutes with a standard deviation of 18 minutes. Test the engineer's claim that the new batteries run longer than the old. Use a 0.01 level of significance.

a. Claims:

b. Check Assumptions:

c. Test:

d. Compare:

e. Conclusion: