Hypothesis Testing Variance

Hypothesis testing is the use of statistics  found in the probability that a specified hypothesis is correct. Hypothesis is specified as declaration which may or may not be accurate. In statistics two hypothesis testing are used. They are null hypothesis and alternative hypothesis. These two hypothesis tested are opposed to each other. In statistics the significance level is symbolized through alpha. Let us see about the probability of hypothesis testing variance.

Hypothesis testing variance

There are five constituent to either statistical test:

Null Hypothesis

Alternate Hypothesis

Test Statistic

Level of significance

Conclusion

Hypothesis testing variance

Consider the population is standard, we are able to test the variance of the method using the chi-square distribution through (n – 1) degrees of freedom.

To test a variance or standard deviation of a population to be exact normally distributed, we can utilize the χ2–test.

The χ2- test for a variance or standard deviation is not as robust as the samples for the population mean otherwise the population proportion.

Therefore it is necessary to while performing the χ2–test used for a variance that the population is usually circulated. The results can be deceptive if the population is not standard.

Examples for hypothesis testing variance

χ2- test for population variance

In a sample of size 16 drawn from a normal population standard deviation is 4 can you say that population standard deviation is 5.

Solution

Null hypothesis:

H0: The population standard deviation is 5

Test statistic:

χ2   =`(ns^2)/sigma^2` ~ χ2n-1

Level of significance:

α= 0.05 at 5% level of χ2  table values for 16 degrees of freedom is 24.996

Calculation:

n = 16, s = 4, σ = 5

χ2   =`(16xx16)/25 = 256/25`

χ2   = 10.24

Calculated value = 10.24

Table value = 24.996

Calculated value < Table value

Therefore the null hypothesis is accepted.

The population standard deviation is 5

Result

The population standard deviation is 5