Show that the significant value of t at level of significance a for one-tailcd test is cqual to that of t at 2α significance level for two-tailed test.

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Camryn Diaz · Accepted Answer

Show that the significant value at t at α for one-tailed test is equal to the significant value at t at 2α for two-tailed test:The critical value at the level of significance α = 0.05 for a one tailed test.The confidence level = (1-α)=0.95Level of significance=α=0.05Let the degrees of freedom = d.f =10Hypothe sis test= one tailedThe critical value is t0.05,10=−1.8125[EXCEL FORMULAT.INV(0.05,10)]For left tailed test, the critical value= -1.8125For right tailed test, the citical value = 1.8125The critical value at the level of significance 2α = 0.1 for a two tailed test.Level of signifi cance =2α=2×0.05 = 0.1Let the degrees of freedom =d.f =10Hypothesi s test= two tailedThe critical value is t0.1,10=0.1825[[EXCEL FORMULAT.INV(0.1,10)]]For two tai led test, the critical value at a = 0.1 is 0.1825To prove that the significant value at t at α for one-tailed test is equal to the significant value at t at 2α for two-tailed test, we have to show that the value at 0.1 in two tailed test is equal to the value at 0.05 in 0ne tailed test.Here, the critical value at 0.05 level of significance in one tail test is 0.1825 and the critical value at 0.1 level of significance in two-tailed test is also 0.1825.Hence, proved that the significant value at t at α level of significance for one-tailed test is equal to the significant value at t at 2α level of significance for two-tailed test.

Show that the significant value of t at level of

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