Question 1207867
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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<ol><li>Reject the null when alpha = 0.05 (since 4.25 > 3.06 is true)</li><li>Reject the null when alpha = 0.025 (since 4.25 > 3.8 is true)</li><li>Fail to reject null when alpha = 0.01 (since 4.25 > 4.89 is false)</li></ol>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
<font color=red>0.01 < pvalue < 0.025</font>


If the p-value is somwehere between 0.01 and 0.025, then we'll meet the conditions mentioned in the instructions.



Answer: <font color=red>option C</font>
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