Question

Chapter 12:

1. What two reasons do we use for the F-Statistic for?

2. What is the critical F value for a hypothesis test with a sample from 5 populations with 20 observations total. Use a .05 significance level.

3. Given a calculated F value of 3.5, would you reject or fail to reject the null hypothesis with the critical F value from question 2?

Answer 1

An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statisticalmodels that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled.

The main use of F-distribution is to test whether two independent samples have been drawn for the normal populations with the same variance, or if two independent estimates of the population variance are homogeneous or not, since it is often desirable to compare two variances rather than two averages.

The test for equality of several means is carried out by the technique called ANOVA.

Here total 5 population

Between df=5-1=4

Total df=20-1=19

Within df=19-4=15

Test statistic=MSB/MSW~F(4,15)

Critical F(4,15) =3.87

Calculated value is 3.5

Since calculated value is less than tabulated value so we do not reject Ho.