Questions: Find the value of t for a t-distribution with 20 degrees of freedom such that the area to the left of t equals 0.025. Round your answer to three decimal places, if necessary.

Find the value of t for a t-distribution with 20 degrees of freedom such that the area to the left of t equals 0.025. Round your answer to three decimal places, if necessary.

Transcript text: Find the value of $t$ for a $t$-distribution with 20 degrees of freedom such that the area to the left of $t$ equals 0.025. Round your answer to three decimal places, if necessary.

Solution

Solution Steps

Step 1: Identify the Given Parameters

Degrees of Freedom ($n$): 20 Specified Probability Value ($P$): 0.025 Direction/Area Specification: Area to the left of $-t$

Step 2: Use $t$-Distribution

Since we are looking for the area to the left of $-t$, we use the CDF of the $t$-distribution to find the $t$ value.

Step 3: Calculation

Using the CDF, we find the $t$ value for $P = 0.025$ and $n = 20$.

Final Answer:

The $t$ value for a $t$-distribution with 20 degrees of freedom and a probability of 0.025 to the left is approximately -2.086.

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