Question 7 of 13, Step 2 of 2 Consider the value of \( t \) such that the area under the curve between - \( |t| \) and \( |t| \) equals 0.9 . Stesson: 8.2 Student's t-distrinuturn table. 2 : Assuming the degrees of freedom equals 5 , select the \( t \)-value from the \( t \)-distribution tablect
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To find the \( t \)-value from the t-distribution table for degrees of freedom (df) of 5, where the area under the curve between \( -|t| \) and \( |t| \) equals 0.9, you're looking for the critical values where the two tails combined represent the remaining area (0.1). This means you want to find the \( t \)-value that corresponds to an area of 0.05 in each tail (0.1 total). According to the t-distribution table for df = 5, the critical \( t \)-value that corresponds to an area of 0.05 in one tail is approximately 2.571. The range would thus be from \( -2.571 \) to \( 2.571 \). You can confidently use \( t = 2.571 \) here since it satisfies the requirement of covering an area of 0.9 between the two critical points!
