Application {17 marks & Communication {8 marks} 1. Identify the likely outlier in this set of data by circling it and write as an ordered pair (x,y). {2A marks } X 17 103 93 54 44 33 26 Y 22 118 19 64 53 40 312. List the type of correlation and causal relationship that you would expect to find for each of the following pairs of variables. { 2 A & 2 C marks } Scenario Type of Correlation Choose ONE or TWO Possible Causal (Positive/Negative, Relationships { common-cause factor, Strong/Weak) cause-and-effect, accidental, reverse cause-and-effect, presumed relationship} Price of Gasoline at the pump vs. current world price of Crude Oil Parent's Education Level vs. Children's Success in School 3. A car manufacturer tested the gap between the doors and the body of a car. Thirty samples were taken at the factory and their gaps were recorded (in mm), are shown in the table below. STATE THE TYPE OF TECHNOLOGY USED (or website) DO NOT DO CALCULATIONS BY HAND unless otherwise stated! {13 A marks}. (1) 1.7 1.9 1.4 1.1 1.4 1.5 1.1 1.2 1.6 1.9 1.8 1.4 1.5 1.2 1.1 1.6 1.5 1.3 1.8 1.7 1.2 1.0 1.7 1.6 1.6 1.8 1.6 1.2 1.1 1.9 a) Find the median, first quartile, third quartile, range and interquartile range for these gap measurements in millimetres. (5A) b) Create a box & whisker plot for the data by hand or using technology. {import or screen capture one from program or website used } (2A)c) Calculate the mean, standard deviation, and variance for gap (in mm) found between the doors and the body of a car. (3A) d) Use the z-score formula to calculate by hand the z-score for the price of : (2A) i) gap with 1.7 mm ii) door with a gap of 1.1 mm? e) If the Quality Control Inspector rejects any cars with gaps that are not within 2 standard deviations of the mean, how many of the cars in this sample would be rejected? Show your work. (20) 4. Does the slope of the line of best fit tell you anything about the strength of a linear correlation? Explain why or why not. (2 C) 5. What does the correlation coefficient tell you? Explain the scale used to measure the strength of the correlation coefficient, highlighting key values where the interpretation changes. (2C)