Homework 4 – Due November 10, 2015 Problem 1

QUESTION

Homework 4 – Due November 10, 2015Problem 1 (by hand)In a length of hospitalization study conducted by several cooperating hospitals, a random sample of 24peptic ulcer patients was drawn from a list of all peptic ulcer patients ever admitted to the participatinghospitals and the length of hospitalization per admission was determined for each. The mean length ofhospitalization per admission was found to be 8.15 with a standard deviation of 3 days. Assume that thelength of hospitalization of peptic ulcer patients is approximately normally distributed.(a) Construct and interpret a 90% confidence interval for the true length of stay for peptic ulcer patients.(b) Based on other studies we can say that the true length of stay for duodenal ulcer patients is 9 days.Do we have sufficient evidence in the data to conclude that the length of stay for peptic ulcerpatients is significantly lower than duodenal ulcer patients? (Define the parameter(s), state thehypotheses, fix alpha, compute the test statistic and the p-value, and state the decision andconclusion in the context of the problem).Problem 2 (using SAS; include SAS commands and SAS output)Some studies of Alzheimer’s disease (AD) have shown an increase in CO2 production in patients with thedisease. In one such study the following CO2 values were obtained from 12 neocortical biopsy samplesfrom AD patients.100812801181123515482362195610801458205217561350(a) Compute a 95% confidence interval for the true mean CO2 value in AD patients. Interpret it in thecontext of the problem.(b) Do we have sufficient evidence in the data to conclude that the true average CO2 value in ADpatients is different from 1100? (Define the parameter(s), state the hypotheses, fix alpha, give thevalue of the test statistic and the p-value, and state your decision and conclusion in the context of theproblem).(c) Do we have sufficient evidence in the data that the true average CO2 value in AD patients is below2000? (Define the parameter(s), state the hypotheses, fix alpha, give the value of test statistic and thep-value, and state your decision and conclusion in the context of the problem).(d) Discuss if the parametric methods used in parts (a)-(c) are appropriate. Justify your answer.1

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