The (t) distribution with 1 degree of freedom is given by [f(t)=frac{1}{pi}left(1+t^{2} ight)^{-1} quad-infty Verify the value

The \(t\) distribution with 1 degree of freedom is given by

\[f(t)=\frac{1}{\pi}\left(1+t^{2}\right)^{-1} \quad-\infty

Verify the value given for \(t_{0.05}\) for \(v=1\) in Table 4 .

Data From Table 4

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Table 4 Values of ta 0 ta = 0.10 = 0.05 = 0.025 = 0.01 =0.00833 a = 0.00625 = 0.005 1 3.078. 6.314 12.706 31.821 38.204 50.923 63.657 2 1.886 2.920 4.303 6.965 7.650 8.860 9.925 12 2 3 1.638 2.353 3.182 4.541 4.857 5.392 5.841 3 4 1.533 2.132 2.776 3.747 3.961 4.315 4.604 5 10 1.476 2.015 2.571 3.365 3.534 3.810 4.032 45 4 6 1.440 1.943 2.447 3.143 3.288 3.521 3.707 6 7 1.415 1.895 2.365 2.998 3.128 3.335 3.499 7 8 1.397 1.860 2.306 2.896 3.016 3.206 3.355 8 9 1.383 1.833 2.262 2.821 2.934 3.111 3.250 9 10 1.372 1.812 2.228 2.764 2.870 3.038 3.169 10