Discuss the below:
Q. A random sample of 500 measurements on the length of stay in hospitals had sample mean 5.4 days and sample standard deviation 3.1 days. A federal regulatory agency hypothesizes that the average length of stay is in excess of 5 days.
a. Do the data support this hypothesis? Use α= 0.05.
b. Construct a 98% confidence interval from the data, and test the hypothesis with the confidence interval. Is the conclusion the same as in part a?
c. For α= 0.05, calculate β when μa = 5.5, and determine the power of the test at this value of μa.
d. How large should the sample size be if we require that α= 0.01 and β= 0.05 when μa = 5.5?