Question

T/F

(4) If a sample gives strong enough evidence to reject the null at the 5% level, it will also give strong enough evince to reject the null at the 1% level.

(5) A smaller p value gives us stronger evidence against the null hypothesis.

Answer 1

(4)

Explanation :

The rejection rule for 1% significance level is, if p-value <= α (=0.01) then reject the null hypothesis and for 5% significance level p-value  α (=0.05).

If the p-value is less than 0.01 then it would obviously be less than 0.05.

But if the p-value is less than 0.05 then there is only a small chance that it will be less than 0.01.

So, the given statement is FALSE

(5)

Explanation :

lets say p-value is 0.001 which is very smaller value.

As we can see that p-value is 0.001 which is very small and it is less than 0.005 which means we can reject null hypothesis at 99.5% confidence level.

I.e. the p-value gives the strong evidence against the null hypothesis because it is small.

So, the given statement is TRUE

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