2 A newspaper article claimed that "taller dog owners have taller dogs as pets". Alex investigated this claim and obtained data from a random sample of 16 fellow students who owned exactly one dog. The results are summarised as follows, where the height of the student, in cm, is denoted by \(h\) and the height, in cm, of their dog is denoted by \(d\).
\(\mathrm { n } = 16 \quad \sum \mathrm {~h} = 2880 \quad \sum \mathrm {~d} = 660 \quad \sum \mathrm {~h} ^ { 2 } = 519276 \quad \sum \mathrm {~d} ^ { 2 } = 30000 \quad \sum \mathrm { hd } = 119425\)

1. Calculate the value of Pearson's product moment correlation coefficient for the data.
2. State what your answer tells you about a scatter diagram illustrating the data.
3. Use the data to test, at the \(5 \%\) significance level, the claim of the newspaper article.
4. Explain whether the answer to part (a) would be likely to be different if the dogs' weights had been used instead of their heights.