Question

after running a hypothesis test, there was evidence to support the mean final percent for all students was less than 80%. concerned that this might be a problem, I found the mean final percent for all students to be 80%. What type of error is this?

Answer 1

Solution:

Given: after running a hypothesis test, there was evidence to support the mean final percent for all students was less than 80%.

For given test procedure, null and alternative hypothesis can be written as:

$H_{0}: \mu = 80 \%$

Vs

$H_{1}: \mu < 80 \%$

Since null is always equal type and alternative hypothesis is either < or > or not equal to type.

Actual or in reality mean final percent for all students to be 80%.

So here we have made decision of mean final percent for all students was less than 80%, that means we have rejected null hypothesis $H_{0}: \mu = 80 \%$ and accepted its alternative hypothesis $H_{1}: \mu < 80 \%$ , but in fact  mean final percent for all students to be 80%, that means null hypothesis $H_{0}: \mu = 80 \%$ is true.

So here we have rejected null hypothesis H0, in fact it is true.

Following are the definitions of Type 1 , Type 2 and correct decision.

Type 1 Error : Reject null hypothesis , in fact it is True.

Type 2 Error : Fail to reject null hypothesis , in fact it is False.

Correct decision: Reject H0, when it is False  or   Fail to reject H0, when it is True.

Thus according to definition , Type I error is occurred.

Thus correct answer is: Type I Error