Question

Identify the following statements as true or false.

Part 1 of 4
If P=0.04, the result is statistically significant at the 0.02 level.
The statement is (Choose one) .
Part 2 of 4 If P = 0.04, the null hypothesis is rejected at the a=0.02 level.
The statement is (Choose one) .
Part 3 of 4 If P=0.04, the result is statistically significant at the a 0.05 level.
The statement is (Choose one)
Part 4 of 4 If P=0.04, the null hypothesis is rejected at the 0.05 level.
The statement is (Choose one)

Answer 1

The statements are: False, True, False, True.

Step-by-step explanation:

Part 1 of 4: False

Part 2 of 4: True

Part 3 of 4: False

Part 4 of 4: True

The answer to each statement is as follows:

1. The result is not statistically significant at the 0.02 level because the p-value is greater than the significance level.
2. The null hypothesis is rejected at the a=0.02 level because the p-value is less than the significance level.
3. The result is not statistically significant at the a=0.05 level because the p-value is greater than the significance level.
4. The null hypothesis is rejected at the 0.05 level because the p-value is less than the significance level.

Answer 2

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.