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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 6

Question

Math 6010 • Linear Models Spring 2015 • Question 6

Suppose we have two samples of sizes \(n_1=4\) and \(n_2=6\). We observe \[ (x_1,x_2,x_3,x_4)=(3.7,3.3,4.2,3.1) \] and \[ (y_1,y_2,y_3,y_4,y_5,y_6)=(3.6,5.0,4.5,3.9,5.1,4.7). \] The null hypothesis is that \(F_X=F_Y\) and the alternative hypothesis is that \(X\) is stochastically smaller than \(Y\). Use the Wilcoxon/Mann–Whitney test. Determine the value of the test statistic and evaluate the p-value of the data. Do not use a large-sample approximation.

Raw LaTeX

Suppose we have two samples of sizes \(n_1=4\) and \(n_2=6\). We observe
\[
(x_1,x_2,x_3,x_4)=(3.7,3.3,4.2,3.1)
\]
and
\[
(y_1,y_2,y_3,y_4,y_5,y_6)=(3.6,5.0,4.5,3.9,5.1,4.7).
\]
The null hypothesis is that \(F_X=F_Y\) and the alternative hypothesis is that \(X\)
is stochastically smaller than \(Y\). Use the Wilcoxon/Mann--Whitney test.
Determine the value of the test statistic and evaluate the p-value of the data.
Do not use a large-sample approximation.

Topic Tags

F-Tests and t-Tests Uniform Integrability and Truncation Methods