Question 5 6 pts You collect the data for your study, and you get the following values: She collects the following data: - Group A: $\bar{x}_{1}=60.16, s_{1}^{2}=8.25, \mathrm{n}_{1}=20$ - Group B: $\bar{x}_{2}=86.72, s_{2}^{2}=73.24, \mathrm{n}_{2}=20$ What is the $t$-statistic for this test? (Write your answer below, to two decimal places as a positive value; sign doesn't matter)

Step 1 ：The t-statistic is calculated using the formula: \(t = \frac{{\bar{x}_1 - \bar{x}_2}}{{\sqrt{{\frac{{s_1^2}}{{n_1}} + \frac{{s_2^2}}{{n_2}}}}}}\)

Step 2 ：Substitute the given values into the formula: \(t = \frac{{60.16 - 86.72}}{{\sqrt{{\frac{{8.25}}{{20}} + \frac{{73.24}}{{20}}}}}}\)

Step 3 ：Simplify the numerator: \(t = \frac{{-26.56}}{{\sqrt{{\frac{{8.25}}{{20}} + \frac{{73.24}}{{20}}}}}}\)

Step 4 ：Simplify the denominator: \(t = \frac{{-26.56}}{{\sqrt{{0.4125 + 3.662}}}}\)

Step 5 ：Calculate the square root: \(t = \frac{{-26.56}}{{2.0183}}\)

Step 6 ：Finally, calculate the t-statistic: \(t = -13.16\)

Step 7 ：Since the question asks for the absolute value, the t-statistic is \(\boxed{13.16}\)