# T Test and Z test Significance level

For a two tail T test at 0.05 significance level and 23 degree of freedom.

Do I take T value at half ofp= 0.05 (0.025) to estimate my value or confidence interval?

Were as for Z test at 0.05 I take the Z value at p=0.05 which is 1.96?

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Yes, for two tail test you need to take half. 0.05 = 0.025 left and 0.025 right

below is from CFA text book

On either side of the acceptance region is a rejection region (or critical region). If the null hypothesis that μ = μ

_{0}is true, the test statistic has a 2.5 percent chance of falling in the left rejection region and a 2.5 percent chance of falling in the right rejection region. Any calculated value of the test statistic that falls in either of these two regions causes us to reject the null hypothesis at the 0.05 significance level. The rejection points of 1.96 and −1.96 are seen to be the dividing lines between the acceptance and rejection regionsThanks for the reply. Follow up question

Do I take half of significance for one tail T test and significance value for one tail Z test?

Thanks

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For a one-tailed T-test or Z-test you would just look up the correct value based on the significance level. You would not need to divide by 2.

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Keith Lo

Product Manager at AdaptPrep

https://www.adaptprep.com/cfa

Thank you

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Very helpful explanation, thank you!

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