compyac

2022-05-01

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

Camryn Diaz

Beginner2022-05-02Added 14 answers

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$\alpha$ = 0.05 for a one tailed test.

The confidence level = (1-$\alpha$ )=0.95

Level of significance=$\alpha$ =0.05

Let the degrees of freedom = d.f =10

Hypothe sis test= one tailed

The critical value is${t}_{0.05,10}=-1.8125$ $\left[\begin{array}{c}EXCEL\text{}FORMULA\\ T.INV(0.05,10)\end{array}\right]$

For left tailed test, the critical value= -1.8125

For right tailed test, the citical value = 1.8125

The critical value at the level of significance 2$\alpha$ = 0.1 for a two tailed test.

Level of signifi cance =2$\alpha$ =2$\times$ 0.05 = 0.1

Let the degrees of freedom =$d.f$ =10

Hypothesi s test= two tailed

The critical value is${t}_{0.1,10}=0.1825$ $\left[\begin{array}{c}\left[\begin{array}{c}EXCEL\text{}FORMULA\\ T.INV(0.1,10)\end{array}\right]\end{array}\right]$

For two tai led test, the critical value at a = 0.1 is 0.1825

To 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.

The critical value at the level of significance

The confidence level = (1-

Level of significance=

Let the degrees of freedom = d.f =10

Hypothe sis test= one tailed

The critical value is

For left tailed test, the critical value= -1.8125

For right tailed test, the citical value = 1.8125

The critical value at the level of significance 2

Level of signifi cance =2

Let the degrees of freedom =

Hypothesi s test= two tailed

The critical value is

For two tai led test, the critical value at a = 0.1 is 0.1825

To 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.

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