Calculate the test-statistic, $t$ with the following information.
\[
\begin{array}{l}
n_{1}=20, \bar{x}_{1}=2.04, s_{1}=0.71 \\
n_{2}=35, \bar{a}_{2}=1.89, s_{2}=0.2
\end{array}
\]
Rounded to 2 decimal places.
Answer
Final Answer: The test-statistic, \(t\) is \(\boxed{0.92}\)
Step 1 ：Given the following values: \(n_{1}=20\), \(\bar{x}_{1}=2.04\), \(s_{1}=0.71\), \(n_{2}=35\), \(\bar{x}_{2}=1.89\), \(s_{2}=0.2\)
Step 2 ：We calculate the test-statistic, \(t\), 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 3 ：Substituting the given values into the formula, we get: \(t = \frac{2.04 - 1.89}{\sqrt{\frac{0.71^{2}}{20} + \frac{0.2^{2}}{35}}}\)
Step 4 ：Solving the above expression, we get \(t = 0.92\)
Step 5 ：Final Answer: The test-statistic, \(t\) is \(\boxed{0.92}\)
