A financial planner wants to compare the yield of income- and growth-oriented mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income-oriented and 40 growth-oriented funds. The mean increase for a two-year period for the income funds is $1100. For the growth?oriented funds the mean increase is $1090. At the 0.01 significance level is there a difference in the mean yield of the two funds? Assume that ?₁ = $45 and ?₂ = $55. State your work in the 5-step hypothesis test.