Final answer:
The statement regarding statistical significance at the 0.02 level and rejecting the null hypothesis at that level are both false as P=0.04 is greater than 0.02. However, at the 0.05 level, both the statement about statistical significance and rejecting the null hypothesis are true since P=0.04 is less than 0.05.
Step-by-step explanation:
When considering whether the result of a statistical test is significant or if the null hypothesis should be rejected, we compare the p-value with the predetermined level of significance, commonly represented by α (alpha).
Part 1: If P=0.04, the result is statistically significant at the 0.02 level. This statement is false because the p-value is greater than the significance level of 0.02, meaning the result is not statistically significant at that level.
Part 2: If P = 0.04, the null hypothesis is rejected at the α=0.02 level. This statement is false for the same reason as above; the p-value does not justify rejecting the null hypothesis at this stricter significance level.
Part 3: If P=0.04, the result is statistically significant at the α 0.05 level. This statement is true. Since the p-value is less than the significance level of 0.05, the result is significant at this level.
Part 4: If P=0.04, the null hypothesis is rejected at the 0.05 level. This statement is also true, as rejection of the null hypothesis is warranted when the p-value is lower than the chosen significance level.