- A researcher claims that, at a river bend, the water gradually gets deeper as the distance from the inner bank increases. He measures the distance from the inner bank, \(b \mathrm {~cm}\), and the depth of a river, \(s \mathrm {~cm}\), at 7 positions. The results are shown in the table below.
| Position | A | B | C | D | E | F | G |
| Distance from | | inner bank \(\boldsymbol { b } \mathbf { c m }\) |
| 100 | 200 | 300 | 400 | 500 | 600 | 700 |
| Depth \(\boldsymbol { s } \mathbf { c m }\) | 60 | 75 | 85 | 76 | 110 | 120 | 104 |
The Spearman's rank correlation coefficient between \(b\) and \(s\) is \(\frac { 6 } { 7 }\)
- Stating your hypotheses clearly, test whether or not the data provides support for the researcher's claim. Use a \(1 \%\) level of significance.
- Without re-calculating the correlation coefficient, explain how the Spearman's rank correlation coefficient would change if
- the depth for G is 109 instead of 104
- an extra value H with distance from the inner bank of 800 cm and depth 130 cm is included.
The researcher decided to collect extra data and found that there were now many tied ranks.
- Describe how you would find the correlation with many tied ranks.