QuestionAugust 27, 2025

Use the critical value t^ast =2.056 and alpha =0.05 to find the following probability. P(tgt -2.056)=[?]

Use the critical value t^ast =2.056 and alpha =0.05 to find the following probability. P(tgt -2.056)=[?]
Use the critical value t^ast =2.056 and alpha =0.05 to find the following probability. P(tgt -2.056)=[?]

Solution
4.2(265 votes)

Answer

0.975 Explanation 1. Understand the distribution The t-distribution is symmetric around 0. For \alpha = 0.05, we are interested in the probability of t being greater than a negative critical value. 2. Calculate the probability Since P(t > -2.056) is equivalent to 1 - P(t \leq -2.056), and given the symmetry, P(t \leq -2.056) = \frac{\alpha}{2} = 0.025. Thus, P(t > -2.056) = 1 - 0.025.

Explanation

1. Understand the distribution<br /> The $t$-distribution is symmetric around 0. For $\alpha = 0.05$, we are interested in the probability of $t$ being greater than a negative critical value.<br />2. Calculate the probability<br /> Since $P(t > -2.056)$ is equivalent to $1 - P(t \leq -2.056)$, and given the symmetry, $P(t \leq -2.056) = \frac{\alpha}{2} = 0.025$. Thus, $P(t > -2.056) = 1 - 0.025$.
Click to rate:

Similar Questions