What is the approximate permutation test p-value

Reference no: EM138178

1. Consider a small experiment to investigate if biofeedback can reduce blood pressure. Six subjects were randomized to the treatment group (n=2) and the control group (n=4) and the difference in blood pressure before and after biofeedback/control treatment is recorded as follows:

The test statistics will be the observed difference in the sample means. There are 15 possible permutations. Here is the sorted list of test statistics:

What is the permutation test P-value for testing the equality of the means versus the hypothesis that the mean change for the treatment group is larger than the mean treatment for the control group?
A. 0.067
B. 0.133
C. 0.933
D. 0/05

2. An inventor claims that a new invention increases gas mileage by 4%. A test of the device was done by randomly selecting 10 cars (of the same make and model) that were fitted with the device and 10 cars that served as a control. These 20 cars were randomized to drivers and the mileage (mpg) was recorded for each car. A permutation test was used to test if the mean mileage using the device was greater than the mean mileage of the control group. The following figure presents a histogram of the permutation test differences in means (test control) based on 1000 permutations. The dark vertical line is the observed test statistic.

What is the approximate permutation test P-value?
A. 0.20
B. 0.15
C. 0.85
D. 1.0

Reference no: EM138178

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