Math 503

Lab: Small sample tests

I. Using the Sign test, Wilcoxon Signed Rank test, and the t-test to test a hypothesis concerning the golf data set.

A. Use HELP to find the description of the golf data set. (Print the description).

B. Open the golf data set.

The data set is located at L:\MTBWin\student9/golf.mtb

C. This student claims that, on average, his score for 9 holes of golf is under 45. Assuming these 22 games represent a random sample of his games, is there evidence to support his claim that his average score is below 45?

1. Test hypotheses using t-test

use stat 6 basic stat 6 1 sample t-test

Select c1

enter 45 in the test mean window

click on options

click on arrow next to alternative window

click on >less than=

click OK

click OK

2. Test hypotheses using sign test

use stat 6 nonparametrics 6 1- sample sign

Select c1

check Test Median

enter 45 for the median

click on arrow next to alternative window

click on >less than=

click OK

3. Test hypotheses using Wilcoxon test

use stat 6 nonparametrics 6 1- sample Wilcoxon

Select c1

check Test Median

enter 45 for the median

click on arrow next to alternative window

click on >less than=

click OK

4. Make your conclusion based on these test results. How do the p-value for each test compare? Do all of the above tests lead to the same conclusion? Which test do you believe is the most reliable or the best to apply in this case? Explain.

II. Checking for normality of the population. Use the golf data set and check for normality of the student=s scores.

A. A normal probability plot

Use Graph6probability plot

Select C1 as variable

keep assumed distribution as normal (default)

Click OK

Print the Normal Plot

B. Normality Tests (Normal probability plot is also provided with each in MINITAB).

use stat 6 basic stat 6 normality test

Select c1 as variable

click OK

Print the normal plot with the test result

(By default the Anderson-Darling test for normality will be performed).

To see the Ryan-Joiner or Kolmogorov-Smirnov, tests repeat part B above, but select the desired test before clicking OK.

Exercise: Go to the k:\school\Henson\math\math213. Open the file called Samples.MTW. For each sample provided, check or test for normality of the population and apply all three tests (sign, Wilcoxon, and t ) to test μ=2 vs. μ…2. Discuss the appropriateness or inappropriateness of each test and compare results.