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If the between-groups and within-groups variance estimates are close, F will be near one and the null hypothesis is:
AFirmly rejected
BAutomatically true
CImpossible to test
DNot contradicted
Answer & Solution
Correct answer: D. Not contradicted
1. The F ratio compares two estimates of the same population variance.
2. Variance between samples and variance within samples both estimate the population variance.
3. If they agree, their ratio F sits near one.
4. But if F is much larger than one, then the evidence is against the null hypothesis.
5. So an F near one leaves the null hypothesis uncontradicted.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 13 'The F Distribution and One-Way ANOVA', sections 13.1-13.4_
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