# Whether the given statement mean that the two populations cannot have same mean

Whether the given statement mean that the two populations cannot have same mean or not.
Given: The null hypothesis is false in case of One-way ANOVA test.
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Given: The null hypothesis is false in case of One-way ANOVA test.
Calculation:
The null hypothesis is false does not mean that the two populations cannot have the same mean.
The hypothesis for one way ANOVA is given below:
Null Hypothesis:
${H}_{0}:{\mu }_{1}={\mu }_{2}={\mu }_{3}\dots \dots \dots \dots \dots \dots \dots ={\mu }_{k}$
Alternative hypothesis:
${H}_{a}$ : At least one of the mean is different.
One way ANOVA is basically used to compare more than two groups of means. The null hypothesis is false really mean that "At least one of then is different", but not any two of the populations have the same mean.