10 A researcher plans to carry out a statistical investigation to test whether there is linear correlation between the time ( \(T\) weeks) from conception to birth, and the birth weight ( \(W\) grams) of new-born babies.
- Explain why a 1-tail test is appropriate in this context.
The researcher records the values of \(T\) and \(W\) for a random sample of 11 babies. They calculate Pearson's product-moment correlation coefficient for the sample and find that the value is 0.722 .
- Use the table below to carry out the test at the \(1 \%\) significance level.
\section*{Critical values of Pearson's product-moment correlation coefficient.}
| \multirow{2}{*}{} | 1-tail test | 5\% | 2.5\% | 1\% | 0.5\% |
| 2-tail test | 10\% | 5\% | 2.5\% | 1\% |
| \multirow{4}{*}{\(n\)} | 10 | 0.5494 | 0.6319 | 0.7155 | 0.7646 |
| 11 | 0.5214 | 0.6021 | 0.6851 | 0.7348 |
| 12 | 0.4973 | 0.5760 | 0.6581 | 0.7079 |
| 13 | 0.4762 | 0.5529 | 0.6339 | 0.6835 |