Hv0 : u = 35 versus Hv1 : u doesn't not equal 35

Question

The true value is 40 and Hv0 is not rejected

Is this a type 1 error, type 2 error or correct

Answer 1

In hypothesis testing, we define the hypotheses as follows:

• Null Hypothesis (\(H_0\)): \(u = 35\)
• Alternative Hypothesis (\(H_1\)): \(u \neq 35\)

In this scenario, you stated that the true value is 40. Therefore:

• The null hypothesis (\(H_0\)) is actually false (since 40 is not equal to 35).
• You failed to reject the null hypothesis.

This situation is classified as a Type II error. A Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, you are incorrectly concluding that the mean is equal to 35 when it is actually 40.