8. In an experiment designed to study the effects of illumination level on task performance, 9 subjects were required to insert a fine-tipped probe into the cycholes of a needle both under a low light level with black background and a high light level with a white background. Let X1, X2. .... Xe be the time used by the 9 subjects to insert a fine-tipped probe into the eyeholes of a needle under a low light level with black background, and Y1, Y2,.... Yo be the time used by the same 9 subjects to insert a fine-tipped probe into the cycholes of a needle under high light level with a white background. X1, X2. ..., Xo are assumed to follow Normal(1, of), and Y1. Y2, ..., Yo are assumed to follow Normal(/12, 07), where of and of are unknown. The data are shown in the following table. (Hint: the critical values are Zoozs = 1.96, Zo.0s = 1.64, 60.025,8 = 2.31, to.05,8 = 1.86, 60.025,9 = 2.26, loos9 = 1.83) Subjects 1 2 3 4 5 6 7 9 Black 25.01 41.05 27.47 25.74 24.96 28.84 25.85 20.89 32.05 White 16.61 24.98 24.59 19.68 16.07 20.84 18.23 19.50 22.96 (a) (5') Compute the 95% two-sided confidence interval for / - /42. (b) (5') Define Ho : /1 = /42, and Ha : /1 > /42. Implement the hypothesis test with the level 5%