The yield of a chemical process expressed in percentage of the theoretical maximum is measured with each of two catalyst a and b and with no catalyst(control c). five observation are made under each condition making the usual assumption for an analysis of variance test the hypothesis that there is no difference in main yield between the three condition. use the 5% level of significance a(79.2,80.1,77.4,77.6,77.8). b(81.5,80.7,80.5,81.7,80.6). c(74.8,76.5,74.7,74.8,74.9).

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?