What is the sampling distribution to test the ratio of variances?
A test of two variances hypothesis test determines if two variances are the same. The distribution for the hypothesis test is the F distribution with two different degrees of freedom. Assumptions: The populations from which the two samples are drawn are normally distributed.
What is the relation between population variance and variance of sample distribution?
Summary: Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data.
Is the sample mean and population variance the same?
And just by chance all samples have exactly the same value–not very likely but not impossible either. The sample mean is of course the identical value of each sample drawn. But the sample variance is zero. So the ratio of the sample variance to the population variance is also zero.
How is the variance of the f ratio calculated?
To calculate the F ratio, two estimates of the variance are made. Variance between samples: An estimate of σ2 that is the variance of the sample means multiplied by n (when the sample sizes are the same.). If the samples are different sizes, the variance between samples is weighted to account for the different sample sizes.
Which is the distribution of the sample mean?
That’s because the sample mean is normally distributed with mean \\(\\mu\\) and variance \\(\\frac{\\sigma^2}{n}\\). Therefore: \\(Z=\\dfrac{\\bar{X}-\\mu}{\\sigma/\\sqrt{n}}\\sim N(0,1)\\)
Is it possible to get a zero sample variance?
As noted in the original question, a zero sample variance would imply a zero probability of occurrence because the ratio of the sample variance to the population variance times n-1 is Chi Square distributed. Yet it is possible to get such an outcome.