Question

Where 90% of the area falls between these two t values with 29 degrees of freedom, and both t values are the same distance from 0 smaller value?

Option 1: -1.699
Option 2: 1.699
Option 3: -2.045
Option 4: 2.045

Answer 1

Critical t-values for a t-distribution with 29 degrees of freedom and 5% in each tail are -2.045 and 2.045, which are equidistant from 0.

Step-by-step explanation:

The student is asking about t-values for a t-distribution with 29 degrees of freedom where 90% of the area falls between two critical values that are equidistant from 0. To find these critical values, one typically uses a t-distribution table or a statistical calculator function such as invT. Given that 90% of the area is in the center, we are dealing with a two-tailed test where the remaining 10% is split equally in two tails, with 5% in each tail. The critical t-value for a two-tailed test with 29 degrees of freedom and α = 0.05 (5%) is 2.045, meaning the critical values are -2.045 and 2.045. Thus, the correct t values that meet the criteria described would be Option 3: -2.045 and Option 4: 2.045.