91影视

The critical value of r needs to be computed using the given formula.

The degrees of freedom are given to be equal to n-2. The sample size (n) is equal to 27 and the level of significance \(\left( \alpha \right)\) is equal to 0.02. \(\)

The critical value can be computed using the formula given below.

\(r = \frac{t}{{\sqrt {{t^2} + n - 2} }}\)

Where

t is the critical value obtained from t distribution table with n-2 degrees of freedom and\(\alpha = 0.02\)

n is the sample size and has a value equal to 27.

Referring to the t distribution table, the critical value of t with 25 degrees of freedom for 0.02 significance level is 2.4851.

The critical value is computed as shown below:

\(\begin{aligned} r &= \frac{t}{{\sqrt {{t^2} + n - 2} }}\\ &= \frac{{2.4851}}{{\sqrt {{{\left( {2.4851} \right)}^2} + 27 - 2} }}\\ &= 0.445\end{aligned}\)

Thus, the critical r values are -0.445 and 0.445.