Part: \( 1 / 3 \) Part 2 of 3 If the true value of \( \mu \) is 71 , is the result a Type I error, a Type II error, or a correct decision? The result is a \( \square \) correct decision .

To determine whether the result is a Type I error, a Type II error, or a correct decision, we need to understand the definitions of these errors in the context of hypothesis testing: 1. **Type I Error**: This occurs when the null hypothesis is rejected when it is actually true. In other words, we conclude that there is an effect or a difference when there is none. 2. **Type II Error**: This occurs when the null hypothesis is not rejected when it is actually false. This means we fail to detect an effect or a difference that actually exists. 3. **Correct Decision**: This occurs when we correctly reject the null hypothesis when it is false or correctly fail to reject the null hypothesis when it is true. Given that the true value of \( \mu \) is 71, we need to know what the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \)) are in this context. Typically, we might have: - \( H_0: \mu = 71 \) (the null hypothesis states that the true mean is 71) - \( H_a: \mu \neq 71 \) (the alternative hypothesis states that the true mean is not 71) Now, if the result of the hypothesis test leads us to reject \( H_0 \) (concluding that \( \mu \) is not 71), but the true value is indeed 71, then we have made a Type I error. Conversely, if we fail to reject \( H_0 \) (concluding that \( \mu \) is 71) and the true value is indeed 71, then we have made a correct decision. Since the true value of \( \mu \) is given as 71, if the result indicates that we do not reject \( H_0 \), then it is a correct decision. Thus, the result is a \( \text{correct decision} \).