Question

Consider the value of t such that the area under the curve between −|t| and |t| equals 0.9.

Assuming the degrees of freedom equals 25, select the t value from the t table.

Answer 1

Given that, degrees of freedom = 25

We want to find, the t-score such that, P(-t0 < t < t0) = 0.9

P(-t0 < t < t0) = 0.9

=> 2 * P(t < t0) - 1 = 0.9

=> 2 * P(t < t0) = 1.9

=> P(t < t0) = 1.9/2

=> P(t < t0) = 0.95

Using t-table we get, t-score corresponding probability of 0.95 or 0.05 at 25 degrees of freedom is, t = 1.708

In t-table we find, t-score corresponding 25 degrees of freedom and two-tail area of 0.10 is t = 1.708

=> P(-1.708 < t < 1.708) = 0.9

Hence, we get, -|t| = -1.708 and |t| = 1.708