A random sample was taken of 20 patients admitted to a hospital with a certain diagnosis. The lengths of stays in days for the 20 patients were 4, 2, 4, 7, 1, 5, 3, 2, 2, 4 5, 2, 5, 3, 1, 4, 3, 1, 1, 3

a Calculate a 95% confidence interval (use the methodSE) for the mean length of hospital stay. Is your answer reasonable? What underlying assumptions were required for this method and are they reasonable? b. Calculate a 95% percentile bootstrap interval and interpret. c. Refer to the previous problem. Take logs of the data (base "e") Calculate a 95% confidence interval for the mean of the log length of stay.

d. Take antilogs (exponential) of the endpoints of the confidence interval found in part a.. Explain why that is a 95% confidence interval for the median length of stay if the data is lognormally distributed (lognormally distributed is when the logarithm of the data points has a normal distribution). Technically, under the lognormal assumption, is the confidence interval that you found in this equation also a confidence interval for the mean length of stay?