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 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. (ii) Power + P(Type II Error) = 1. (iii) 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 1

Solution:

Part i)

We are given that: 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

We know: Level of significance is the probability of type II error.

and Type II error is defined as reject null hypothesis H0, in fact H0 is true.

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 ii)

We are given that: Power + P(Type II Error) = 1

Since power of the test is given by formula:

Power = 1 - P(Type II Error)

thus we get:

Power + P(Type II Error) = 1

Thus given statement is TRUE.

Part iii)

We are given that: 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.

We know that: Level of significance is the probability of rejecting null hypothesis in fact it is true.

Thus if level of significance increases, then 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.