Math / Data & Statistics

QuestionFor a confidence level of $98 \%$ with a sample size of 21 , find the critical $t$ -value (also known as the $t$ -score). $\square$ (round to 3 decimal places)

Studdy Solution

STEP 1

1. The sample size is 21.
2. The confidence level is 98%.
3. The degrees of freedom for a $t$ -distribution is $n - 1$ , where $n$ is the sample size.

STEP 2

1. Calculate the degrees of freedom.
2. Determine the critical $t$ -value using the $t$ -distribution table or calculator.

STEP 3

Calculate the degrees of freedom:
$\text{Degrees of freedom} = n - 1 = 21 - 1 = 20$

STEP 4

For a confidence level of 98%, the significance level $\alpha$ is $1 - 0.98 = 0.02$ . Since this is a two-tailed test, divide $\alpha$ by 2:
$\frac{0.02}{2} = 0.01$

STEP 5

Using a $t$ -distribution table or calculator, find the critical $t$ -value for 20 degrees of freedom and a significance level of 0.01 in each tail.
The critical $t$ -value is approximately:
$\boxed{2.528}$
The critical $t$ -value is:
$\boxed{2.528}$

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QuestionFor a confidence level of $98 \%$ with a sample size of 21 , find the critical $t$ -value (also known as the $t$ -score). $\square$ (round to 3 decimal places)

Studdy Solution

STEP 1

1. The sample size is 21.
2. The confidence level is 98%.
3. The degrees of freedom for a $t$ -distribution is $n - 1$ , where $n$ is the sample size.

STEP 2

1. Calculate the degrees of freedom.
2. Determine the critical $t$ -value using the $t$ -distribution table or calculator.

STEP 3

Calculate the degrees of freedom:
$\text{Degrees of freedom} = n - 1 = 21 - 1 = 20$

STEP 4

For a confidence level of 98%, the significance level $\alpha$ is $1 - 0.98 = 0.02$ . Since this is a two-tailed test, divide $\alpha$ by 2:
$\frac{0.02}{2} = 0.01$

STEP 5

Using a $t$ -distribution table or calculator, find the critical $t$ -value for 20 degrees of freedom and a significance level of 0.01 in each tail.
The critical $t$ -value is approximately:
$\boxed{2.528}$
The critical $t$ -value is:
$\boxed{2.528}$

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QuestionFor a confidence level of 98%98 \%98% with a sample size of 21 , find the critical ttt-value (also known as the ttt-score). □\square□ (round to 3 decimal places)

Studdy Solution

STEP 1

1. The sample size is 21.2. The confidence level is 98%.3. The degrees of freedom for a t t t-distribution is n−1 n - 1 n−1, where n n n is the sample size.

STEP 2

1. Calculate the degrees of freedom.2. Determine the critical t t t-value using the t t t-distribution table or calculator.

STEP 3

Calculate the degrees of freedom:Degrees of freedom=n−1=21−1=20 \text{Degrees of freedom} = n - 1 = 21 - 1 = 20 Degrees of freedom=n−1=21−1=20

STEP 4

For a confidence level of 98%, the significance level α\alphaα is 1−0.98=0.021 - 0.98 = 0.021−0.98=0.02. Since this is a two-tailed test, divide α\alphaα by 2:0.022=0.01 \frac{0.02}{2} = 0.01 20.02​=0.01

STEP 5

Using a t t t-distribution table or calculator, find the critical t t t-value for 20 degrees of freedom and a significance level of 0.01 in each tail.The critical t t t-value is approximately:2.528 \boxed{2.528} 2.528​ The critical t t t-value is:2.528 \boxed{2.528} 2.528​

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

QuestionFor a confidence level of $98 \%$ with a sample size of 21 , find the critical $t$ -value (also known as the $t$ -score). $\square$ (round to 3 decimal places)

1. The sample size is 21.
2. The confidence level is 98%.
3. The degrees of freedom for a $t$ -distribution is $n - 1$ , where $n$ is the sample size.

1. Calculate the degrees of freedom.
2. Determine the critical $t$ -value using the $t$ -distribution table or calculator.

Calculate the degrees of freedom:
$\text{Degrees of freedom} = n - 1 = 21 - 1 = 20$

For a confidence level of 98%, the significance level $\alpha$ is $1 - 0.98 = 0.02$ . Since this is a two-tailed test, divide $\alpha$ by 2:
$\frac{0.02}{2} = 0.01$

Using a $t$ -distribution table or calculator, find the critical $t$ -value for 20 degrees of freedom and a significance level of 0.01 in each tail.
The critical $t$ -value is approximately:
$\boxed{2.528}$
The critical $t$ -value is:
$\boxed{2.528}$