Please include step-by-step explanation and show formulas used. Please use R to solve the problem as appropriate.

In comparing the times until failure (in hours) of two different types of light bulbs, we obtain the sample characteristics n1 = 45, x = 984, s2 = 8, 742 and n2 = 52, y = 1, 121, $2 = 9, 411. Test the hypothesis that the average duration of the second type of light bulbs is higher than the first type. at significance level a = 0.05