- 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
His results are shown in the scatter diagram on the next page.
- Describe the correlation between \(x\) and \(y\).
Marc suggests that parents with long last names tend to give their children shorter first names.
- Using the scatter diagram comment on Marc's suggestion, giving a reason for your answer.
The results from Marc's random sample of 16 observations are given in the table below.
| \(x\) | 3 | 6 | 8 | 7 | 5 | 3 | 11 | 3 | 4 | 5 | 4 | 9 | 7 | 10 | 6 | 6 |
| \(y\) | 7 | 7 | 4 | 4 | 6 | 8 | 5 | 5 | 8 | 4 | 7 | 4 | 5 | 5 | 6 | 3 |
- Use your calculator to find the product moment correlation coefficient between \(x\) and \(y\) for these data.
- Test whether or not there is evidence of a negative correlation between the number of letters in the last name and the number of letters in the first name.
You should
- state your hypotheses clearly
- use a \(5 \%\) level of significance
\section*{Question 2 continued.}
\includegraphics[max width=\textwidth, alt={}]{10736735-3050-43eb-9e76-011ca6fa48b8-05_1125_1337_294_372}
\section*{Question 2 continued.}
\section*{Question 2 continued.}