Consider an hypothetical clinical trial that wishes to employ two statistical () tests to assess the hypothesis at both an interim point in time and at the completion of the study (where the population standard deviation can be considered known and equivalent for both tests).
Call the test statistic from the first interim analysis and the test statistic at the completion of the study
a) A total of 25 patients were enrolled at the time of the interim analysis, (sample mean outcome = ), with an additional 11 patients enrolled between the interim analysis and the completion of the study, (sample mean outcome for the patients= Using the known standard deviation, write the second test statistic as a function of. [Hint: The $$-stat for any $Z$-test is]. [5 marks]
b) The test statistic at the interim analysis was. If the mean of the observed outcomes for the 11 patients recruited between the interim analysis and the final analysis was 1.9, is the null hypothesis rejected or retained using a Bonferroni procedure to control the familywise error rate at 0.05? [3 marks]
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