Save \& Exit Certify Lesson: 8.2 Student's t.Distribution KASEE GARRETT Question 4 of 13, Step 1 of 1 4/20 Correct Find the value of \( t \) for a \( t \)-distribution with 15 degrees of freedom such that the area to the left of \( t \) equals 0.05 . Round your answer to three decimal places, if necessary. Keypad

To find the value of \( t \) for a t-distribution with 15 degrees of freedom (df) where the area to the left equals 0.05, you'd typically consult a t-table or use statistical software. For df = 15 and a left-tail area of 0.05, the critical value \( t \) is approximately -1.753. This value indicates that only 5% of the distribution's area lies to the left of this critical point. If you were to visualize this on a graph, imagine a curve representing the t-distribution; the area under the curve to the left of -1.753 would be shaded, representing that 5% probability—the scary low threshold for those outliers! So, remember this value as you delve deeper into the mysteries of statistics, as it sets the stage for hypotheses and confidence intervals!