Question

Suppose we test the null hypothesis H0:μ=μ0 against the alternative hypothesis Ha. What is the correct decision at significance level α?

1)Ha:μ≠μ0,α=5%,p=0.001: We (reject or do not reject) the null hypothesis. We (have or do not have) significant evidence that the population mean is (different from, lower than, or higher than) μ0.

2) Ha:μ>μ0,α=10%,p=0.12: We (reject or do not reject) the null hypothesis. We (have or do not have) significant evidence that the population mean is (different from, lower than, or higher than) μ0.

3)Ha:μ>μ0,α=10%,p=0.12: We (reject or do not reject) the null hypothesis. We (have or do not have) significant evidence that the population mean is (different from, lower than, or higher than) μ0.

4)Ha:μ<μ0,α=5%,p=7.32⋅10−8: We (reject or do not reject) the null hypothesis. We (have or do not have) significant evidence that the population mean is (different from, lower than, or higher than) μ0.

Answer 1

The correct decisions at the given significance levels and p-values are outlined.

Step-by-step explanation:

For the given significance levels and p-values, we can make the following decisions:

1. Ha:μ≠μ0, α=5%, p=0.001: We reject the null hypothesis. We have significant evidence that the population mean is different from μ0.
2. Ha:μ>μ0, α=10%, p=0.12: We do not reject the null hypothesis. We do not have significant evidence that the population mean is higher than μ0.
3. Ha:μ>μ0, α=10%, p=0.12: We do not reject the null hypothesis. We do not have significant evidence that the population mean is higher than μ0.
4. Ha:μ<μ0, α=5%, p=7.32⋅10−8: We reject the null hypothesis. We have significant evidence that the population mean is lower than μ0.