8. The MACBAT Company has developed a new NiCad 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 45 new batteries and 55 old batteries. The old batteries run continuously for 163 minutes with a standard deviation of 10 minutes. The new batteries run for 178 minutes with a standard deviation of 15 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: f. If there is a difference, give a confidence interval for the difference in lifetimes of the batteries