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AP Statistics 12.2A Assignment 1. Mrs. Hanrahan’s Pre-Calculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data: Length (cm) 16.5 17.5 19.5 22.5 28.5 31.5 34.5 37.5 43.5 46.5 106.5 Period (s) 0.777 0.839 0.912 0.878 1.004 1.087 1.129 1.111 1.290 1.371 2.115 A. Make a reasonably accurate scatterplot of the data, using length as the explanatory variable. Describe what you see. There is a strong positive slightly curved relationship between length and period with one very unusual point in the top-right corner. B. The theoretical relationship between a pendulum’s length and its period is period 2 g length where g is a constant representing the acceleration due to gravity (in this case, g = 980 cm/s2). Use a transformation to linearize the curved pattern in the graph. The scatterplot shows length vs period. C. Give the equation of the least-squares regression line. Define any variables you use. yˆ 0.086 0.210 x ŷ is the predicted period and x is the length of the pendulum D. Use the model from part C to predict the period of a pendulum with length 80 centimeters. Show your work. yˆ 0.086 0.210 80 1.8 seconds 2. If you have taken a chemistry class, then you are probably familiar with Boyle’s law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant in symbols, PV k . Students collected the following data on pressure and volume using a syringe and a pressure probe. Volume (cubic centimeters) 6 8 10 12 14 16 18 20 Pressure (atmospheres) 2.9589 2.4073 1.9905 1.7249 1.5288 1.3490 1.223 1.1201 A. Make a reasonably accurate scatterplot of the data, using length as the explanatory variable. Describe what you see. There is a strong negative curved relationship between volume and pressure. B. The theoretical relationship between the pressure and volume of the gas is PV k , we can divide both sides of this equation by V to obtain the theoretical model P k 1 , or P k . Use a transformation to linearize the V V curved pattern in the graph. The scatterplot shows 1 vs pressure volume C. Give the equation of the least-squares regression line. Define any variables you use. 15.897 x ŷ is the predicted pressure and x is the volume yˆ 0.368 D. Use the model from part C to predict the pressure in the syringe when the volume is 17 cubic centimeters. Show your work. yˆ 0.368 15.897 1.303 atmospheres 17