P-value for t ≤ 1.76 with 24 degrees of freedom

Question

Quizplus · Accepted Answer

According to a t-distribution table with 24 degrees of freedom, the area under the curve up to t = 1.76 is 0.9544. Since the p-value is the probability of obtaining a t-value as extreme or more extreme than the observed one, we need to find the area under the curve beyond t = 1.76 in both tails, which is 1 - 0.9544 = 0.0456. However, we are only interested in the area in one tail since the alternative hypothesis is not two-sided (it is not clear from the question whether it is a one- or two-tailed test, but we assume a one-tailed test for this explanation). Therefore, the p-value is 0.0456 divided by 2, which gives 0.0228. However, that is not one of the answer choices, so we choose the closest one, which is C) 0.9544.

P-Value for T ≤ 1