Question

IB math studies

1. Ten students were asked for their average grade at the end of their last year of high school and their average grade at the end of their last year at university. The results were put into a table as follows: Student High School grade, University grade, y 90 3.2 2.6 75 80 3.0 70 95 3.8 85 90 3.8 2.8 70 95 85 3.0 3.5 10 Total 835 30.4 (a) Given that s, 8.96, sy-0.610 and sy 4.16, find the correlation coefficient r, giving your answer to two decimal places. (b) Describe the correlation between the high school grades and the university grades. Find the equation of the regression line for y on x in the form y-ax +b. (c) (Total 6 marks) 2. Eight students in Mr. O'Neil's Physical Education class did pushups and situps. Their results are shown in the following table. Student number of pushups () 24 1832 51 342 45 25 number of situps)32 28 3840 30 52 48 52 The graph below shows the results for the first seven students. 60 50 number of 40 situps () 30 20 10 O 10 20 30 40 50 60 number of pushups (x) (a) Plot the results for the eighth student on the graph (b) If x -34 and y 40, draw a line of best fit on the gragh. A student can do 60 pushups. How many situps can the student be expected to do? (c) Working Answers (Total 8arks) 3. The figure below shows the lengths in centimetres of fish found in the net of a small trawler. 10 Number of 6 fish 5 0 20 30 40 50 60 70 80 90 100 110 120130 Length (cm) Find the total number of fish in the net. (a) (b) Find i) the modal length interval; the interval containing the median length: (ii) (i) an estimate of the mean length. Write down an estimate for the standard deviation of the lengths. (i) How many fish (if any) have length greater than three standard deviations above the mean? (ii) The fishing company must pay a fine if more than 10% of the catch have lengths less than 40cm. (d) Do a calculation to decide whether the company is fined A sample of 15 of the fish was weighed. The weight, W was plotted against length, L as shown below. 1,2 W 0.8 (kg) 0.6 0.4 0.2 20 40 60 100 80 (e) Exactly two of the following statements about the plot could be correct. Identify the two correct statements Note: You do not need to enter data in a GDC or to calculate r exactly The value of r, the correlation coefficient, is approximately 0.871. (i) There is an exact linear relation between W and L. (i) (iii) The line of regression of won L has equation w-0012L + 0.008 (iv) There is negative correlation between the length and weight. The t otficica, l aproxinacly 0. (vi) The line of regression of W'on L has equation W -63.5L + 16.5. (Total 14 marks) The following table gives the amount of fuel in a car's fuel tank, and the number of kilometres travelled after filling the tank. Distance 0 220 276500 680 850 travelled (km) Amount of fuel in tank (litres) 43 30 24 10 (a) On the scatter diagram below, plot the remaining points. Fuel in litres 0 100 200 300 400 300 600 700 800 900 1000 Distance in km The mean distance travelled is 421 km ), and the mean amount of fuel in the tank is 28 litres (y). This point is plotted on the scatter diagram. Sketch the line of best fit. (b) A car travelled 350 km. Use your line of best fit to estimate the amount of fuel left in the tank. (c) Working Answer (Total 6 marks) The sketches below represent scatter diagrams for the way in which variables x, y and z change over time, 5. t i a given chemical experiment. They are labelled , and time r time ime State which of the diagrams indicate that the pair of variables (a) (i) is not correlated shows strong linear correlation. (ii) (b) A student is given a piece of paper with five numbers written on it. She is told that three of these numbers are the product moment correlation coefficients for the three pairs of variables shown above. The five numbers are 0.9, -0.85, 0.20, 0.04, 1.60 6) For each sketch above state which of these five numbers is the most appropriate value for the correlation coefficient. (i) For the two remaining numbers, state why you reject them for this experiment. (Total 7 marks)

Answer 1

60 40 20 . :30 10 Mi ooB0o