Statistical Methods

Unit 6 - Small samples Tests (n <30)

6.1.1. Case study 1
Test of hypothesis based on t- distribution are discussed below
CASE 1:Test for Single Mean
Let x1, x2 ...xn are a random sample of size n drawn from a normal population with mean µ. Let and s² denote mean and variance of the sample.
To test the hypothesis the following test procedure is used:



This test statistic follows t -distribution with (n-1) degree of freedom.

(iii) Statistical decision

If the table value of t at 5% level of significance, then reject H_o at 5% level of significance. Otherwise accept H_o

If the table value of t at 1% level of significance, then reject H_o at 1% level of significance. Otherwise accept H<sub>o

Example 1: A sample of 25 fingerlings drawn from a rearing tank showed a mean length of 75.8 mm and standard deviation of 10 mm. Is the data consistent with the claimed mean size of 80 mm?

Answer: Let µ denote the population mean</sub>

(iii) Statistical decision
The table values of t with 24 degrees of freedom are 2.064 at 5% and 2.797 at 1% level of significance. Since is greater the table value of t at 5% level H_o is rejected at 5% level, but as less than the table value of t at 1% level, H_o is not rejected at 1% level of significance.