Single Population Variance:

The variable consists of a chi-square distribution when the population variance consists of a normal distribution. The degree of freedom is (n-1). We can utilize this to test the population variance beneath some conditions.

Conditions for testing:

a) The population consists of a normal distribution.

b) The data is from arbitrary sample

c) The observations should be independent of one other.

d) The test statistic consists of a chi-square distribution with (n-1) degree of freedom and is provided by:

χ² = (df . s²)/σ²

The testing is done in similar way as before. Keep in mind that, all hypothesis testing is completed beneath the supposition that null hypothesis is true.

Confidence Intervals:

Whenever you resolve the test statistic formula for the population variance, you acquire:

σ² = (df . s²)/ χ²

a) Determine the two critical values (that is, alpha/2 and 1-alpha/2)

b) Calculate the value for population variance that is given above.

c) Put the population variance among the two values computed in step 2 (place the smaller one first).

Note that the left-hand end-point of confidence interval comes whenever the right critical value is employed and the right-hand end-point of confidence interval comes whenever the left critical value is utilized. This is as critical values are in the denominator and therefore dividing by the maximum critical value (that is, right tail) provides the smaller end-point.

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