### 7.5.3 Testing the mean with the T test: studentt

The studentt command will examine whether data conforms to Student’s distribution. For small sample sizes, the studentt test is preferable to normalt. You need to provide the studentt command with the following arguments:

1. The sample data information can be given as a list [ns,ne] consisting of the number of successes ns and the number of trials ne, or a list [m,t] consisting of the mean m and the sample size t, or a data list of the sample.
2. The mean of the population to or a data list from a control sample.
3. The standard deviation of the population. If the data list from a control sample is provided, then this item is unnecessary.
4. The type of test; "!=","<" or ">".
5. The confidence level. This is optional; the default value is 0.05.

The studentt command will return the result of a T test. It will return 0 if the test fails, 1 if the test succeeds, and it will display a summary of the test.

If you enter

studentt([10,20], 0.5, 0.02, ’!=’, 0.1)

you will get

       *** TEST RESULT 0 ***
       Summary T-Test null hypothesis H0 mu1=mu2, alt. hyp. H1 mu1!=mu2.
       Test returns 0 if probability to observe data is less than 0.1
       (null hyp. mu1=mu2 rejected with less than alpha probability error)
       Test returns 1 otherwise (can not reject null hypothesis)
       Data mean mu1=10, population mean mu2=0.5, degrees of freedom 20
       alpha level 0.1, multiplier*stddev/sqrt(sample size)= 1.32534*0.02/4.47214
       0

If you enter

studentt([0.48,20],0.5,0.1,’<’)

you will get

       *** TEST RESULT 1 ***
       Summary T-Test null hypothesis H0 mu1=mu2, alt. hyp. H1 mu1<mu2.
       Test returns 0 if probability to observe data is less than 0.05
       (null hyp. mu1=mu2 rejected with less than alpha probability error)
       Test returns 1 otherwise (can not reject null hypothesis)
       Data mean mu1=0.48, population mean mu2=0.5, degrees of freedom 20
       alpha level 0.05, multiplier*stddev/sqrt(sample size)= 1.72472*0.1/4.47214
       1