Question

The correct sampling distribution used when making inferences about a single population's variance is a(n) _____ distribution.

	a) F
	b) χ2
	c) t
	d) normal

Answer 1

Here in this Question the option B is correct.

B) Chi square distribution.

Explanation : when we have to test the single population Variance to compare it to specific Variance we have to use chi square test Statistic at n-1 degrees of freedom.

Assumptions :

The sample must be random.

The underlying distribution is Normal.

The test stat has a chi square dist. with n-1 degrees of freedom and is given by:

The assumptions are the underlying distribution is Normal. The following test will be used,

Hypothesis:

• 
• 

test statistic is:

where:

• n = the total number of observations in the sample data
• s2 = sample variance
• = hypothesized value of the population variancVariance.  

Now we computed the critical value using chi square table .

Decision Rule : we Reject Ho null hypothesis when test Statistic fall in critical region.

This is the hypothesis test for testing one population Variance.

Other options are incorrect for this scenario.

Thank you.