Step 1 :State the appropriate null and alternate hypotheses. The null hypothesis \(H_{0}: \mu_{1}=\mu_{2}\) and the alternate hypothesis \(H_{1}: \mu_{1}>\mu_{2}\). This is a right-tailed test.
Step 2 :Calculate the degrees of freedom using the simple method. The formula for degrees of freedom is \(df = n1 + n2 - 2\).
Step 3 :Substitute the given values into the formula. Here, \(n1 = 41\) and \(n2 = 46\). So, \(df = 41 + 46 - 2\).
Step 4 :Simplify the expression to find the degrees of freedom. So, \(df = 85\).
Step 5 :The degrees of freedom using the simple method is \(\boxed{85}\).