This is a two-tailed test, so we are concerned about the critical values that give a total area of 0.05 in both the upper and lower tails. Therefore, each tail will have an area equal to half of 0.05, or 0.025. Any test statistic greater than or equal to the positive critical value or less than or equal to the negative critical value will result in the null hypothesis being rejected. An excerpt of the t table with 57 degrees of freedom is given below.Degreesof FreedomArea in Upper Tail0.200.100.050.0250.010.005570.8481.2971.6722.0022.3942.665Move along the row for 57 degrees of freedom until reaching the column corresponding to an upper tail area of 0.025. This value of t will be the positive critical value. Find this value, rounding the results to three decimal places.t =The second critical value will be the opposite sign of the positive one just found. Therefore, the critical values for the rejection rule, to three decimal places, are as follows.test statistic ≤test statistic ≥

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Description: This is a two-tailed test, so we are concerned about the critical values that give a total area of 0.05 in both the upper and lower tails. Therefore, each tail will have an area equal to half of 0.05, or 0.025. Any test statistic greater than or equa

The level of significance is α = 0.05.

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This is a two-tailed test, so we are concerned about the critical values that give a total area of 0.05 in both the upper and lower tails. Therefore, each tail will have an area equal to half of 0.05, or 0.025. Any test statistic greater than or equal to the positive critical value or less than or equal to the negative critical value will result in the null hypothesis being rejected. An excerpt of the t table with 57 degrees of freedom is given below.

Degrees of Freedom	Area in Upper Tail
0.20	0.10	0.05	0.025	0.01	0.005
57	0.848	1.297	1.672	2.002	2.394	2.665

Move along the row for 57 degrees of freedom until reaching the column corresponding to an upper tail area of 0.025. This value of t will be the positive critical value. Find this value, rounding the results to three decimal places.

t =

The second critical value will be the opposite sign of the positive one just found. Therefore, the critical values for the rejection rule, to three decimal places, are as follows.

test statistic ≤test statistic ≥

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