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Null hypothesis of a one-way ANOVA is that the means are equal. Alternate hypothesis a one-way ANOVA is that at least one of the means are different.
Yes, in fact, that is one of ANOVA's chief uses.
Yes anova can and should be used to predict correlation between variable's in a single group. This is one of the primary and most common uses of such software.
No, F can never be smaller than 1; it can equal 1.
The F-test is designed to test if two population variances are equal. It compares the ratio of two variances. If the variances are equal, the ratio of the variances will be 1.The F-test provides the basis for ANOVA which can compare two or more groups.One-way (or one-factor) ANOVA: Tests the hypothesis that means from two or more samples are equal.Two-way (or two-factor) ANOVA: Simultaneously tests the hypothesis that the means of two variables from two or more groups are equal.