Marc took a random sample of 16 students from a school and for each student recorded - the number of letters, x, in their last name - the number of letters, y, in their first name - Edexcel - A-Level Maths Statistics - Question 2 - 2021 - Paper 1

Marc's suggestion that parents with long last names tend to give their children shorter first names is supported by the scatter diagram. The points show a downward trend, indicating a negative correlation. As the x-values (last name length) increase, the y-values (first name length) generally decrease.

The product moment correlation coefficient, denoted as $r$, is calculated to be approximately $-0.545$. This negative value indicates a moderate negative correlation between the lengths of last names and first names.

To test the hypothesis, let:

• $H_0$: $ho = 0$ (no correlation)
• $H_1$: $ho < 0$ (negative correlation)

Given the significance level of 5%, we compute the correlation coefficient. The computed value of $r$ is $-0.545$. The critical value for a one-tailed test at n-2 degrees of freedom (14) is approximately $-0.497$. Since $-0.545$ is less than $-0.497$, we reject $H_0$. This provides evidence of a significant negative correlation between the lengths of the last names and first names.