Test of Two Variances Quiz

PDF page 728: Another use of the F distribution is testing two variances. It is often desirable to compare two variances rather than two averages. For instance, college administrators would like two college professors grading exams to have the same variation in their grading. For a lid to fit a container, the variation in the lid and the container should be the same. A supermarket might be interested in the variability of check-out times for two checkers. To perform a F test of two variances, it is important that the following are true:

PDF page 728: • The populations from which the two samples are drawn are normally distributed.

PDF page 728: • The two populations are independent of each other.

PDF page 728: sample variances, we use the F ratio

PDF page 728: F has the distribution F ~ F(n1 – 1, n2 – 1), where n1 – 1 are the degrees of freedom for the numerator and n2 – 1 are the degrees of freedom for the denominator.

PDF page 728: F has the distribution F ~ F(n1 – 1, n2 – 1), where n1 – 1 are the degrees of freedom for the numerator and n2 – 1 are the degrees of freedom for the denominator.

PDF page 728: If the two populations have equal variances, then and are close in value and

PDF page 728: is close to 1. But if the two

PDF page 728: population variances are very different, and tend to be very different, too. Choosing as the larger sample

PDF page 728: to be greater than 1. If and are far apart, then

PDF page 728: Therefore, if F is close to 1, the evidence favors the null hypothesis (the two population variances are equal). But if F is much larger than 1, then the evidence is against the null hypothesis. A test of two variances may be left-tailed, righttailed, or two-tailed.

PDF page 728: Therefore, if F is close to 1, the evidence favors the null hypothesis (the two population variances are equal). But if F is much larger than 1, then the evidence is against the null hypothesis. A test of two variances may be left-tailed, righttailed, or two-tailed.

PDF page 728: Therefore, if F is close to 1, the evidence favors the null hypothesis (the two population variances are equal). But if F is much larger than 1, then the evidence is against the null hypothesis. A test of two variances may be left-tailed, righttailed, or two-tailed.

PDF page 729: Problem Two college instructors are interested in whethe there is any variation in the way they grade math exams. They each grade the same set of 30 exams. The first instructor’s grades have a variance of 52.3. The second instructor’s grades have a variance of 89.9. Test the claim that the first instructor’s variance is smaller. In most colleges, it is desirable for the variances of exam grades to be nearly the same among instructors. The level of significance is 10 percent. Solution Let 1 and 2 be the subscripts that indicate the first and second instructor, respectively.