# Subject(s): Mathematics–Applied Statistics

Subject(s): Mathematics–Applied Statistics

You should test :

1- generate data for Normal Dist. and generate data for Exponential Dist.

2- Moses test for variance

3- The Mann-Whitney test.

you should follow description in attached

Description of job

You should use SAS program only to write the code

What I am going to have you work on is Moses technique for testing for variances. We can start off on using this for two samples and then extend it to k samples where k is greater than 2. We will start off assuming samples of size 18 from each population and then samples of size 36 from each population. We will apply the Moses technique to test for differences in variances of the two populations. We will first use the Moses technique using subsamples of size 3 and then subsamples of size 6. We want to compare the alpha values and powers of these tests for subsamples of size 3 and then for subsamples of size 6 when are initial samples sizes are of size 18, and then when they are of size 36. We will be finding these when the underlying populations are normal, and then when they are exponential. We will compare the powers of the Moses (both with 3 and 6 subsample size) with the powers of the F test for two populations. (Eventually, we will expand to more than two populations.)

You can start by sampling from normal populations. Let’s first estimate the alpha levels – have both populations be normal with mean 10 and variance 25. We would have samples of size 18 from each – using Moses technique – break these into subsamples of size 3 each, and then of size 6 each. Calculate the Moses test for subsamples of size 3 each and then subsamples of size 6 each. Also, calculate the F test. Do this for 5000 samples and keep track of when you get a rejection from each test. The estimated type 1 error for each of the tests will be the number of times each test rejected divided by 5000. We then want to start estimating powers. We can begin this by keeping the means the same for both populations and then changing the variances. Say population 1 is normal with mean 10 and variance 25 and population 2 is normal with mean 10 and variance 36. Again, generate 5000 sets of samples of size 18 each from the two populations and keep track of the numbers of times each test rejects divided by 5000. We would then try to estimate power when the mean changes as well as the variance. Say, the first population has mean 10 and variance 25, an the second population has mean 15 and variance 36. Estimate the powers of all 3 tests.

We will then extend the above to samples of size 36, then also look at exponential populations, and then extend the number of populations. This is a start.

You should the code include :

1- generate data for Normal Dist. and generate data for Exponential Dist.

2- Moses’ test for variance

3- The Mann-Whitney test.