Elementary Statistics and Computer Application

Conditions for the validity of x-test

Conditions for the validity of -test

1. -test is an approximate test for large values of ‘n’ for the validity of -test of goodness of fit between theory and experiment, the following conditions must be satisfied.
2. The sample observations should be independent.
3. Constraints on the cell freqrequency, if any, should be linear.
4. 
5. N, the total frequency should be reasonably large, say greater then (>) 50.
6. No theoretical cell frequency should be less than (<)5. If any theoretical cell frequency is <5, then for the application of - test, it is pooled with the preceding or scecceeding frequency so that the pooled frequency is more than 5 and finally adjust for degree’s of freedom lost in pooling.

Example-1

• The number of yiest cells counted in a haemocytometer is compared to the theoretical value is given below. Does the experimental result support the theory?


Solution:

• H0: the experimental results support the theory
• H1: the esperimental results does not support the theory.
• Level of significance=5%
Test Statistic:





=3.1779

Table value
(6-1=5 at 5 % l.os)= 11.070

Inference

• < tab
• We accept the null hypothesis.
• (i.e) there is a good correspondence between theory and experiment