Question

Find the critical value of t for a sample size 27 and a 99% confidence level?

Answer 1

Answer:

The critical value is T = 2.7787

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$. So we have T = 2.7787

The critical value is T = 2.7787

Answer 2

The critical values define the values to cut-off in a region where the test statistic does not belong

The critical value is $\mathbf{-2.778715}$

The given parameters are:

$\mathbf{n = 27}$

$\mathbf{CL = 99\%}$

First, we calculate the significance level

$\mathbf{\alpha = \frac{1 - CL}{2}}$

Substitute 99% for CL

$\mathbf{\alpha = \frac{1 - 99\%}{2}}$

Express percentage as decimal

$\mathbf{\alpha = 1 - \frac{1 - 0.99}{2}}$

$\mathbf{\alpha =1 - \frac{0.01}{2}}$

$\mathbf{\alpha = 1 - 0.005}$

$\mathbf{\alpha = 0.995}$

Next, calculate the degrees of freedom

$\mathbf{df = n -1}$

Substitute 27 for n

$\mathbf{df = 27 -1}$

$\mathbf{df = 26}$

At $\mathbf{df = 26}$ and $\mathbf{\alpha = 0.995}$, the critical value is -2.778715

So, we have:

$\mathbf{t_c = -2.778715}$

Hence, the critical value is $\mathbf{-2.778715}$

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