Final answer:
An F sampling distribution is used to compare random data with our F sample to conduct a test of two variances, assessing if there is a significant difference between the variances of two independent samples. The F statistic generated from the sample data is compared to the F distribution to infer the likelihood of variances being equal under the assumption of normality in the underlying populations.
Step-by-step explanation:
We find a F sampling distribution for random data to compare it to our F sample because it helps to determine if there are significant differences in variability or variance between two independent samples. This process is necessary when conducting a test of two variances, where the assumption is that the populations are normally distributed, and the samples are independent of each other.
The F statistic, derived from this comparison, is a ratio where the numerator represents the variance of one sample and the denominator represents the variance of another. The comparison is made against the F distribution to determine the p-value, which helps infer if the observed variances are significantly different or not.
Typically, if the F statistic is close to 1, this indicates support for the null hypothesis that the two population variances are equal; if it's much larger than 1, it suggests that the variances are different, hence rejecting the null hypothesis. However, it is important to note that the F test is sensitive to the assumption of normality; significant deviations can affect the test's reliability.