in a length of hospitalization study conducted by several

Problem 1 (by hand)

In a length of hospitalization study conducted by several cooperating hospitals, a random sample of 24 peptic ulcer patients was drawn from a list of all peptic ulcer patients ever admitted to the participating hospitals and the length of hospitalization per admission was determined for each. The mean length of hospitalization per admission was found to be 8.15 with a standard deviation of 3 days. Assume that the length of hospitalization of peptic ulcer patients is approximately normally distributed.

1. Construct and interpret a 90% confidence interval for the true length of stay for peptic ulcer patients.

2. Based on other studies we can say that the true length of stay for duodenal ulcer patients is 9 days. (i)Do we have sufficient evidence in the data to conclude that the length of stay for peptic ulcer patients is significantly lower than duodenal ulcer patients?

3. (Define the parameter(s), state the hypotheses, fix alpha, compute the test statistic and the p-value, and state the decision and conclusion in the context of the problem).