Homework6

Homework6 - 3 Now let’s perform the Mann-Whitney U test using α = 0 05 Our null hypothesis will be that the formulations are equivalent and our

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STA 3024: Homework 6 (due Wednesday Aug 4) Total: 10 points Suppose we’re studying two diﬀerent formulations of ﬂu vaccine. A random sample of nine patients is randomly divided into a group of ﬁve, which receive Formulation 1, and a group of four, which receive Formulation 2. The patients’ response to the ﬂu vaccine is measured and recorded below. Higher values indicate that the vaccine worked better. (The response is measured in terms of “ n -fold increase in antibody response,” but that doesn’t matter.) We want to determine whether or not there is a diﬀerence between how well the two vaccine formulations work. Formulation 1 10.24 3.56 6.60 2.24 3.80 Formulation 2 2.14 1.58 2.12 44.82 1. Explain why the Mann-Whitney U test (test for median) is a better choice than the two-sample t test for analyzing this data. 2. Convert the data into ranks in the appropriate way for the Mann-Whitney U test. Show your answer as a table like the data table above, but with the ranks instead.
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Unformatted text preview: 3. Now let’s perform the Mann-Whitney U test using α = 0 . 05 . Our null hypothesis will be that the formulations are equivalent, and our alternative hypothesis will be that they’re not equivalent (a two-sided alternative). (a) State the assumptions for the Mann-Whitney U test (test for median), and state whether or not they’re satisﬁed for our data. We already stated what our hypotheses were. (b) Calculate the value of the test statistic U . (For the step where you can choose either group, but here choose Formulation 1.) Our test yields a p-value of 0.2857, which is greater than α , so we fail to reject H . (c) Have we proven that the two formulations are equivalent, so that any further research into this question would be a waste of time? Why or why not? (Hint: Just think what fail to reject implies.)...
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This note was uploaded on 12/15/2011 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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