Question

Question 3

Suppose that you are conducting the following test:                                  

Ho: Bill is not guilty.

Ha: Bill is guilty.

How could you commit a Type II error in this test ?

Group of answer choices

by convicting Bill who is actually guilty

by convicting Bill who is actually innocent

by doing nothing

by freeing Bill who is actually innocent

by freeing Bill who is actually guilty

Answer 1

Last Option is correct where type 2 error is committed by freeing Bill who is actually guilty.

Type 1 error occurs when the null hypothesis is rejected even though when it is true(also called false positive).

Bill is not guilty but we are convicting him would be like committing type 1 error as even though null hypothesis is true(i.e, he is not guilty), we are rejecting it and convicting him.

Type 2 error means accepting the null hypothesis even if it is false(also called false negative).

Here the null hypothesis H​​​​​​0 is that Bill is not guilty.

By freeing who is actually guilty will be like convicting type 2 error. T

And, alternative hypothesis H​​​​​​1 is that Bill is guilty.

So, type 2 error will be that we accept the null hypothesis even though it is false. Here, we are accepting null hypothesis even though it is incorrect,i.e we are assuming he is not guilty and freeing him but actually he is guilty so we are making type 2 error.