Question

Which of the following are true? If false, explain briefly.

​a. A very high​ P-value is strong evidence that the null hypothesis is false. ​
b. A very low​ P-value proves that the null hypothesis is false. ​
c. A high​ P-value shows that the null hypothesis is true.
d. A​ P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

Answer 1

The correct options are;

a. False

b. True

c. True

d. False

Explanation:

We look at each of the options as follows

a. A very high p-value is strong evidence that the null hypothesis is false;

The above statement is false because the p-value indicates the likelihood of the null hypothesis being correct, therefore, a high p-value is indicative of the correctness (truth) of the null hypothesis

b. A very low p-value shows that the null hypothesis is false

The above statement is true

c. A high p-value shows that the null hypothesis is true

The above statement is true

d. A P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

The above statement is false as the p-value below which we reject the null hypothesis is dependent on the value of the significance level, α.