If we reject the mill hypothesis can we claim to have proved

If we reject the mill hypothesis, can we claim to have proved that the null hypothesis is false? Why or why not? Choose the correct answer below. A. Not necessarily if the test conditions are satisfied and the p - value is appropriately small, the null hypothesis can only be proven false if the power is appropriately large. B. No, if the p - value is sufficiently small, the null hypothesis is unlikely to be true, but unlikely is not the same as impossible. C. Not necessarily, if the test conditions are satisfied and the p - value is appropriately small, the null hypothesis can only be proven false if the significance level is appropriately small. D. Yes, if the test conditions are satisfied and the p - value is smaller than the significance level, then the null hypothesis is proven to be false.

Solution

No, if the p-value is sufficiently small, the null hypothesis is unlikely to be true, but unlikely is not the same as impossible.