4 Each Each year for eight years, an oil company recorded the number of barrels of oil it produced that year and the total number of active wells it was using by the end of the year. Year Wells Barrels of oil (millions) 2010 2011 46 157 2012 237 337 419 2013 2014 2015 2016 2017 501 601 657 5 21 17 20 25 28 24 30 The company believes that the number of active wells and the number of barrels of oil produced in a year are positively correlated and can be modelled by a linear relationship. Using a 1% significance level, test to see if there is evidence that the company's beliefs are correct. 5 A city council collects data on the population densities in different areas of the city, in people per hectare, and the distances of those areas from the city centre, in km. It calculates the product moment correlation coefficient between the two sets of data and finds it to be -0.51. Given that the council collected data from 24 sample areas, test, at the 1% level of significance, the claim that there is a negative correlation between population density and the distance from the city centre. State your hypotheses clearly. (3 marks) 8 The Mercalli scale and the Richter scale are both used to measure earthquakes. The Mercalli scale is based on structural damage to buildings and the Richter scale is based on the amplitude of the ground vibrations. The table shows data from eight earthquakes. Mercalli intensity, M 9 7 8 6 5 8 6 8 Richter magnitude, R 6.3 5.3 6.0 5.5 4.0 5.4 4.7 7.1 a Calculate, to 3 decimal places, the product moment correlation coefficient between M and R. (1 mark) It is suggested that there is linear correlation between the structural damage and ground vibrations caused by an earthquake. b Test this suggestion at the 1% significance level, stating your null and alternative hypotheses clearly. (3 mark)