MHB Two-tailed Test: Rejecting the Null at 0.05 Level of Significance

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In a two-tailed test with a test statistic value of 2, the probability P(T>2) is 0.03. At a 0.05 significance level, the critical value for each tail is 0.025. Since 0.03 is greater than 0.025, there is insufficient evidence to reject the null hypothesis. The discussion highlights the common confusion in interpreting two-tailed tests and the importance of correctly applying the significance level. Understanding these concepts is crucial for accurate statistical analysis.
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In a two-tailed test, the value of the test statistic is 2. If we know the test statistic follows a Student’s t- distribution with P
(T>2) = 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

I want to say True but I think I'm overthinking the problem. Can anyone help me out?
 
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The problem is, it's a two-tailed test. If you take $0.05$ as your significance level, then you'd need $0.025$ probability in each tail. But your $P$ value is $0.03>0.025$. Therefore, you do not have sufficient statistical evidence to reject the null hypothesis.
 
Yes! I get tripped up working backwards on problems. two-tailed - 0.05/2 = 0.025. I understand - thank you! I feel silly now on such a simple problem.
 

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