Question

classify the conclusion of the hypothesis test as a type i error, a type ii error, or a correct decision.
in 1994, the average math sat score for students at one school was 485. five years later, a teacher wants to perform a hypothesis test to determine whether the average math sat score of students at the school has changed from the 1994 mean of 485. the hypotheses are:
$h_{0}:mu = 485$
$h_{1}:mu
eq485$
suppose that the results of the sampling lead to rejection of the null hypothesis. classify that conclusion as a type i error, a type ii error, or a correct decision, if in fact the average math sat score of students at the school has changed from the 1994 mean of 485.
correct decision
type ii error
type i error

Explanation:

Step1: Recall the definitions

Type I error: Reject \(H_0\) when \(H_0\) is true.
Type II error: Fail to reject \(H_0\) when \(H_0\) is false.
Correct decision: Reject \(H_0\) when \(H_0\) is false or fail to reject \(H_0\) when \(H_0\) is true.

Step2: Analyze the situation

The null hypothesis \(H_0:\mu = 485\) (no change in mean SAT score). The alternative hypothesis \(H_1:\mu
eq485\) (change in mean SAT score).
We rejected \(H_0\), and in fact, the mean has changed (\(H_0\) is false).
Since we rejected \(H_0\) when \(H_0\) is false, this is a correct decision.

Answer:

Correct decision