Question: Total cholesterol levels (X) and body weights (Y) for six subjects are given below.

1. compute \(\sum_{i} x_{i} y_{i}, \sum_{i} x_{i}^{2}, \sum_{i} y_{i}^{2}, \bar{x}\) and \(\bar{y} ;\)
2. compute Pearson's correlation coefficient using the above results;
3. compute the \(t\) -statistic for testing \(H_{0}:\) corr \(=0\) vs. \(H_{A}:\) corr \(\neq 0\)
4. will you reject \(H_{0}\) at the \(5 \%\) level of significance?
5. give your \(\mathrm{p}\) -value for the test in c).
6. produce lists \(\left\{\operatorname{rank}\left(x_{1}\right), \ldots, \operatorname{rank}\left(x_{6}\right)\right\}\) and \(\left\{\operatorname{rank}\left(y_{1}\right), \ldots, \operatorname{rank}\left(y_{6}\right)\right\}\)
7. find Spearman's \(r_{s}\) according to its definition;
8. find Spearman's \(r_{s}\) by using rank differences;
9. using \(r_{s}\) to conduct a similar test as given in part c);
10. report \(p\) -value for the above test;
11. find the precise \(p\) -value by consulting the attached table.

Price: $2.99

Solution: The downloadable solution consists of 5 pages
Deliverable: Word Document