Solved on Jan 03, 2024

Find the tt-value with 12 degrees of freedom such that the right-tailed area is 0.05. Round to 3 decimal places.

STEP 1

Assumptions
1. We are working with a tt-distribution.
2. The degrees of freedom (dfdf) for the tt-distribution is 12.
3. We are looking for the value of tt such that the area to the right of tt is 0.05.
4. The tt-distribution is symmetric about the mean, which is 0.

STEP 2

To find the value of tt for a tt-distribution with a given area to the right, we use a tt-distribution table or a statistical software package that can provide the tt-value associated with a given right-tail probability and degrees of freedom.

STEP 3

Since the tt-distribution is symmetric and we are looking for the area to the right of tt, we are dealing with an upper-tail probability. The area to the right of tt is 0.05, which means we are looking for the tt-value associated with an upper-tail probability of 0.05.

STEP 4

Using a tt-distribution table or statistical software, we find the tt-value that corresponds to an upper-tail probability of 0.05 with 12 degrees of freedom.

STEP 5

The tt-value for 12 degrees of freedom with an upper-tail probability of 0.05 is approximately 1.782.

STEP 6

Round the tt-value to three decimal places, if necessary.
t1.782t \approx 1.782
The value of tt for a tt-distribution with 12 degrees of freedom such that the area to the right of tt equals 0.05 is approximately 1.782.

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