Question

Consider the following statements:

i) Power + P(Type II Error) = 1.

(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) If a hypothesis is tested at the 5% significance level with a given data set, then there is a lower 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.

Determine which of the above statements are true or false.

Answer 1

Solution:

Part i)

Given: Power + P(Type II Error) = 1

Since power of the test is given by:

Power = 1 - P(Type II Error)

thus

Power + P(Type II Error) = 1

Thus given statement is TRUE.

Part ii)

Given:  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

Level of significance is the probability of type II error.

Type II error is Reject null hypothesis H0, in fact H0 is true.

So we have 5% significance level, thus we have 5% probability that null hypothesis will be rejected in fact the null hypothesis is actually true.

Thus given statement is TRUE.

Part iii)

Given:  If a hypothesis is tested at the 5% significance level with a given data set, then there is a lower 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.

Level of significance is the probability of rejecting null hypothesis in fact it is true. Thus as level of significance increases, chance of rejection of null hypothesis increases.

Thus we have more chance of rejecting null hypothesis at 5% significance level as compared to at the 1% significance level.

Thus given statement is FALSE.