Question

Consider the following statements. (i) If a hypothesis is tested at the 5% significance level with a given data set, then there is a higher chance that the null hypothesis will be rejected than if that same hypothesis is tested at the 1% significance level with the same data set. (ii) If a hypothesis test is performed at the 5% significance level, and if the null hypothesis is actually true, then there is a 5% chance that the null hypothesis will be rejected. (iii) P(Type I Error) + P(Type II Error) = 1. Determine which of the above statements are true (1) or false (2).

Answer 1

Solution:

(i) If a hypothesis is tested at the 5% significance level with a given data set, then there is a higher chance that the null hypothesis will be rejected than if that same hypothesis is tested at the 1% significance level with the same data set.

Answer: This statement is false because testing the hypothesis at the 5% level of significance with a given data set will have higher chance of rejecting the null hypothesis then testing the hypothesis at the 1% level of significance with the same data set. The level of significance represents the probability of rejecting the null hypothesis when the null hypothesis is true.

(ii) If a hypothesis test is performed at the 5% significance level, and if the null hypothesis is actually true, then there is a 5% chance that the null hypothesis will be rejected.

Answer: This statement is true because the 5% significance level represents there is 0.05 probability of rejecting the null hypothesis when the null hypothesis is true.

(iii) P(Type I Error) + P(Type II Error) = 1.

Aswer: The given statement is false because P(Type I Error) + P(Type II Error) is always less than 1