Solved on Jan 03, 2024

Find the $t$ -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 $t$ -distribution.
2. The degrees of freedom ( $df$ ) for the $t$ -distribution is 12.
3. We are looking for the value of $t$ such that the area to the right of $t$ is 0.05.
4. The $t$ -distribution is symmetric about the mean, which is 0.

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

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Find the $t$ -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 $t$ -distribution.
2. The degrees of freedom ( $df$ ) for the $t$ -distribution is 12.
3. We are looking for the value of $t$ such that the area to the right of $t$ is 0.05.
4. The $t$ -distribution is symmetric about the mean, which is 0.

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

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

STEP 1

Assumptions1. We are working with a ttt-distribution.2. The degrees of freedom (dfdfdf) for the ttt-distribution is 12.3. We are looking for the value of ttt such that the area to the right of ttt is 0.05.4. The ttt-distribution is symmetric about the mean, which is 0.

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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

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

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

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

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

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