Question

A Company has developed a new battery. The engineer in charge claims that the new battery will operate continuously longer than the old battery. To test the claim, the company selects a simple random sample of 100 new batteries and 100 old batteries. The old batteries run continuously for 190 minutes with a standard deviation of 20 minutes; and the new batteries for 200 minutes with a standard deviation of 40 minutes. 1. Find a 90% confidence interval for the difference in the mean time run of old and new batteries. 2. Test the engineer's claim that the new batteries run longer than the old. U

Answer 1

1. A 90% confidence interval for the difference in mean running time is:
\[(200-190)-1.645\sqrt{\frac{40^{2}}{100}+\frac{20^{2}}{100}}<\mu _{1}-\mu _{2}<(200-190)+1.645\sqrt{\frac{40^{2}}{100}+\frac{20^{2}}{100}}\]
You can calculate the result.