Statistical Methods

Unit 7 - Chi-square distribution

7.7.Test of hypothesis about a population variance
Test of hypothesis about a population variance
Let x₁, x₂ .........................x_n be the values of a variable in a random sample of size n drawn from a normal population with variance σ².
The null hypothesis to be tested is, H_o : σ² = σ_o²
where σ_o² is a specified value.
Test statistic used is

Example 5 : A market survey conducted on 50 households, indicated that the average expenditure of households is Rs.40 per week on purchase of fish with standard deviation of Rs.22. Can this data be considered as a sample from a population with variance of 400 Rs.2, at 5% level of significance?
Answer:
(i) Hypotheses
Ho: σ2 = 400 ; H1 : σ2 ≠ 400
(ii) Test statistic

(iii) Statistical decision
Reject Ho if, > 0.025 or < 0.975
Otherwise do not reject it
For 49 df, 0.025 = 70.222 and 0.975 = 31.555
As lies between 31.555 and 70.222, H_o is not rejected.

Exercise for practice:
I. The following table gives sex-wise eating habit of fish in a random sample of 500 people collected from a city. Does the data support that eating habit of fish depend on sex?

Sex	Number of people
	Eating fish	Not Eating fish
Male	370	150
Female	230	250
Total	600	400

II. A survey of 162 children having one parent with blood group M and another with blood group N revealed that 28.4% children have blood group M 42% have blood group MN and the remaining have the blood group N.Test the validity of the genetic law that the proportion of M: MN: N is 1:2:1