N2025 P2 Q8

N2025 P2 Q8

11 marks
Free

  1. Dilip is investigating how athletes perform in related events. He collects data about the best performances of \(10\) randomly chosen athletes in high jump and long jump. The results, in metres, are shown in the scatter diagram. The correlation coefficient is \(0.39\).

    What do the scatter diagram and correlation coefficient suggest about the relationship between best performance in high jump and long jump amongst athletes taking part in both events? Justify your answer.[2]
  2. \(x\)2.13.96.27.81012.513.815
    \(t\)11265375119165246300
    1. Sketch a scatter diagram of the data. State what the scatter diagram suggests about the relationship between \(x\) and \(t\).[2]

      1. Determine which of the following models is the better fit to the data where \(a\), \(b\), \(c\) and \(d\) are constants.

        \(t=ax+b \qquad t=cx^2+d\)

        [2]

      2. Find the regression equation for the model identified in part (ii)(A).

        [2]

      1. Use the regression equation found in part (ii)(B) to estimate the time Dilip would take for a run of \(11\) km.

        [1]
      2. Give two reasons why your estimate is reliable.[2]
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