If you fail to reject a null hypothesis, can you conclude that the null hypothesis is true? Why or why not?
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If you fail to reject the null hypothesis, you cannot conclude that the null hypothesis is true.
why?
The sample may be too small (low power).
Random variation
There could still be a real difference, but the test wasn’t sensitive enough to detect it.
failing to reject the null hypothesis does not mean it is true, it just means there is not enough evidence against it.
Failing to reject the null hypothesis does not mean it is true; it only means there isn’t enough evidence against it.