Question 1207867: 1) In a one-way ANOVA test, the test statistic is F = 4.25.The rejection region is F > 3.06 for the 5% level of significance, F > 3.8 for the 2.5% level of significance, and F > 4.89 for the 1% level of significance. For this test, which of the following is a valid statement about the approximate p-value?
a) It is between 0.025 and 0.05.
b) It is greater than 0.05.
c) It is between 0.01 and 0.025.
d) It is approximately 0.05.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
F = 4.25 = test statistic
The critical values mentioned for alpha = 0.05, alpha = 0.025, alpha = 0.01 are 3.06, 3.8, 4.89 in that exact order.
Whenever the F test statistic is larger than the F critical value, we are in the rejection region and must reject the null.
Based on the information your teacher gave you, we can set up the following- Reject the null when alpha = 0.05 (since 4.25 > 3.06 is true)
- Reject the null when alpha = 0.025 (since 4.25 > 3.8 is true)
- Fail to reject null when alpha = 0.01 (since 4.25 > 4.89 is false)
I'll refer to these as statements (1) through (3).
The key thing to look for is the change from "reject" to "fail to reject".
This happens when going from statement (2) to statement (3).
If pvalue < 0.025 then we'd reject the null at the level alpha = 0.025
Recall that we reject the null whenever pvalue < alpha.
If pvalue < 0.01 then we'd reject the null at the level alpha = 0.01; but this will flip to "if pvalue > 0.01 then fail to reject the null at alpha = 0.01"
pvalue > 0.01 is the same as saying 0.01 < pvalue
We have found that
0.01 < pvalue and pvalue < 0.025
therefore
0.01 < pvalue < 0.025
If the p-value is somwehere between 0.01 and 0.025, then we'll meet the conditions mentioned in the instructions.
Answer: option C
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