Jacob is leaving his house to go to work and is running 5 minutes late. In the past, when Jacob has been 5 minutes late for work, he has taken an alternate route to work a total of 16 times. When in the same position, Jacob has take his normal route to work 27 times. In the situations when Jacob has taken the alternate route to work, he has been late 8 times, on-time 3 times, and early 5 times. In situations when he has taken his normal route to work, he has been late 9 times, on-time 12 times, and early 6 times.

Based on the information above, if Jacob's goal is to be on-time or early for work, should he take the alternate route or his normal route?

A. find the power of the test, when the null hypothesis assumes a population mean of mu = 450, with a population standard deviation of 156, the sample size is 5 and the true mean is 638.47 with confidence intervals of 95 b. find the power of the test, when the null hypothesis assumes a population mean of mu = 644, with a population standard deviation of 174, the sample size is 3 and the true mean is 744.04 with confidence intervals of 95% c. find the power of the test, when the null hypothesis assumes a population mean of mu = 510, with a population standard deviation of 126, the sample size is 10 and the true mean is 529.44 with confidence intervals of 95