Can someone kindly assist with question with explanation, studying for final exam, much appreciated thank you!

A study was conducted to determine whether a linear relationship exists between the break- ing strength 3; of wooden beams and the specic gravity 3 of the wood. Twelve randomly selected beams of the same crosssectional dimensions were stressed until they broke. The breaking strengths and the density of the wood are shown in the accompanying table for each of the twelve beams. 1 2 3 4 5 6 7 8 9 10 11 12 0.50 0.56 0.60 0.44 0.55 0.53 0.42 0.48 0.41 0.47 0.54 0.65 13.1 12.7 13.1 11.5 12.4 12.6 11.1 11.4 11.0 11.4 12.2 11.5 The following quantities were computed: 12 12 12 2.x.- 2 6.15, 2y.- 2144,21? 2 3.2105, 2y? 2 1734.5,23515. = 74.145. 5:1 i=1 i=1 i=1 i=1 The last pair (0.65, 11.5) was identied as an outlier. Remove this pair from the data set and answer the following questions. (a) Fit the model 1; = o+lx+e That is, use the method of least squares to t a straight line. _6 points] (b) Test H0 : 51 = 0 against the alternative hypothesis, Ha : 31 7E 0, using a = 0.05. 6 points] (c) Find a 95% condence interval for the mean value of y when a: = 0.58. '4 points] (d) Find a 95% prediction interval for y when :17 = 0.58. _4 points]