5 The birth rate, \(x\) per thousand members of the population, and the life expectancy at birth, \(y\) years, in 14 randomly selected African countries are given in the table.
| Country | \(x\) | \(y\) | Country | \(x\) | \(y\) |
| Benin | 4.8 | 59.2 | Mozambique | 5.4 | 54.63 |
| Cameroon | 4.7 | 54.87 | Nigeria | 5.7 | 52.29 |
| Congo | 4.9 | 61.42 | Senegal | 5.1 | 65.81 |
| Gambia | 5.7 | 59.83 | Somalia | 6.5 | 54.88 |
| Liberia | 4.7 | 60.25 | Sudan | 4.4 | 63.08 |
| Malawi | 5.1 | 60.97 | Uganda | 5.8 | 57.25 |
| Mauretania | 4.6 | 62.77 | Zambia | 5.4 | 58.75 |
\(n = 14 , \sum x = 72.8 , \sum y = 826 , \sum x ^ { 2 } = 392.96 , \sum y ^ { 2 } = 48924.54 , \sum x y = 4279.16\)
- Calculate Pearson's product-moment correlation coefficient \(r\) for the data.
- State what would be the effect on the value of \(r\) if the birth rate were given per hundred and not per thousand.
- Explain what the sign of \(r\) tells you about the relationship between life expectancy and birth rate for these countries.
- Test at the \(5 \%\) significance level whether there is correlation between birth rate and life expectancy at birth in African countries.
- A researcher wants to estimate the life expectancy at birth in Zimbabwe, where the birth rate is 3.9 per thousand. Explain whether a reliable estimate could be obtained using the regression line of \(y\) on \(x\) for the given data.