| Part | Answer/Working | Marks | Guidance |
|------|---|---|---|
| (a) | Negative | B1 | B1 for "negative". Allow "slight" or "weak" etc. Allow a description e.g. "as $x$ increases $y$ decreases" or in context e.g. "people with longer last names tend to have shorter first names". A comment of "negative skew" is B0. **Need to see distinct or separate responses for (a) and (b)** |
| (b) | Marc's suggestion is compatible because it's negative correlation | B1 | B1 for a comment that suggests data is compatible with the suggestion and a suitable reason such as "there is negative correlation" or a description in $x$ and $y$ or in context, or the points lie close to a line with negative gradient, or draw line $y = x$ and state that more points below the line so supports (or is compatible with) his suggestion. A reason based on just a **single point** is B0. e.g. "11 letters in last name has only 5 in first name" |
| (c) | $(r =) -0.54458266...$ awrt $\mathbf{-0.545}$ | B1 | B1 for awrt $-0.545$ |
| (d) | $H_0: \rho = 0$ $H_1: \rho < 0$ | B1 | B1 for both hypotheses correct in terms of $\rho$ |
| | $[5\% \text{ 1-tail cv} =] (\pm) 0.4259$ (significant result / reject $H_0$) There is evidence of negative correlation between the number of letters in (or length of) a student's last name and their first name | M1, A1 | M1 for a critical value compatible with their $H_1$: 1-tail: awrt $\pm 0.426$ (condone $\pm 0.425$) or 2-tail (B0 scored for $H_1$) : awrt $\pm 0.497$. If hypotheses are in words and can deduce whether one or two-tail then use their words. If no hypotheses or their $H_1$ is not clearly one or two tail assume one-tail. A1 for compatible signs between cv and $r$ and a correct conclusion in context mentioning **correlation and number of letters or length and name** (if their value from (c)). **Do NOT award this A mark if contradictory statements or working seen** e.g. "accept $H_0$" or comparison of 0.426 with significance level of 0.05 etc. |