Question

For a hypothesis t-test, what is the easiest way to find the p-value (if possible) without using technology? I'm using a two-tailed test and a right-tailed test with t-values = 2.95, n=18 for the two-tailed and t-value = 3.0, n=40 for the right-tailed. Will I be able to calculate the p-values by using table A-3?

Answer 1

The easiest way to find the p-value (if possible) without using technology is using the t-table. The p-value can be obtained from the t table at the specified t-test statistic value and degrees of freedom.

-In the given scenario, it is not specified whether the test is two sample t-test or one sample t-test. So, the degrees of freedom in both the cases is obtained by considering the test is of one –sample t-test.

-Table A-3 signifies t-table.

First:

It is a two-tailed test.

The t-test statistic (t-value) is 2.95.

The sample size (n) is 18.

The degrees of freedom (df) = n – 1 = 18 – 1 = 17

Using t-table, the p-value can be obtained at the t-value = 2.95 and the degrees of freedom =17, as:

Therefore, the p-value is 0.00896.

Second:

It is a right-tailed test.

The t-test statistic (t-value) is 3.0.

The sample size (n) is 40.

The degrees of freedom (df) = n – 1 = 40 – 1 = 39

Using t-table, the p-value can be obtained at the t-value = 3.0 and the degrees of freedom = 39, as:

Therefore, the p-value is 0.0023.