2. A Geography teacher is interested in the link between mathematical ability and the ability to visualise three-dimensional situations. He gives a group of 15 students a test and records each student's score, \(m\), on the mathematics questions and each student's score, \(v\), on the visiospatial questions. He calculates the following summary statistics: $$S _ { m m } = 3747.73 , \quad S _ { v v } = 2791.33 , \quad S _ { m v } = 2564.33$$

1. Calculate the product moment correlation coefficient for these data.
2. Stating your hypotheses clearly and using a \(5 \%\) level of significance test the theory that students who are good at Mathematics tend to have better visio-spatial awareness.
   (4 marks)