Assignment 3, Fall 2000

STATISTICS 403 - Assignment 3

Due Tuesday, September 26, 2000

Use the Wilcoxon signed rank test to analyze the data in problem 3.22 of the text.
A random sample of 20 people who drove automobiles was selected to see if alcohol affected reaction time. Each driver's reaction time was measured in a laboratory before and after drinking a specified amount of beverage containing alcohol. The reaction times in seconds are given below. We are interested in the change in reaction time, Before - After.
```
Driver  Before  After  Driver  Before  After
--------------------------------------------
   1     0.68    0.73    11     0.65    0.72
   2     0.62    0.64    12     0.59    0.60
   3     0.68    0.66    13     0.81    0.78
   4     0.82    0.92    14     0.67    0.66
   5     0.58    0.68    15     0.65    0.68
   6     0.80    0.87    16     0.76    0.77
   7     0.72    0.76    17     0.61    0.72
   8     0.65    0.70    18     0.86    0.86
   9     0.84    0.88    19     0.72    0.74
  10     0.73    0.79    20     0.89    0.97
--------------------------------------------
```
- (a) Considering the differences, Before - After, is symmetry a reasonable assumption? What about normality? Justify your answers statistically.
- (b) Use the one sample t-test to test H:=0 against the alternative A: <0. Be sure to include the value of the test statistic, P-value, decision and a conclusion within the context of the problem.
- (c) Construct a 95% confidence interval on .
- (d) Use the Wilcoxon signed rank test to test H: =0 against the alternative A: <0. Be sure to include the value of the test statistic, P-value, decision and a conclusion within the context of the problem.
- (e) Construct a confidence interval on , with a level of confidence close to 95%, that corresponds to the Wilcoxon signed rank test.
- (f) Use the sign test to test H: = 0 against the alternative A: < 0. Be sure to include the value of the test statistic, P-value, decision and a conclusion within the context of the problem.
- (g) Construct a confidence interval on , with a level of confidence close to 95%, that corresponds to the sign test.
- (h) Compare your results for the three different procedures.
Use the Wilcoxon signed rank test to analyze the data in problem 3.19 of the text. You will need to use average ranks, and a normal approximation with a correction for the use of average ranks.