# Question 1:

## Part (a)

| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| Label all the books from $1 - 160$ (o.e.) | B1 | For labelling/numbering/listing/using sampling frame of all 160 books |
| Use random numbers to select the 10 books | B1 | For use of random numbers/selection and mentioning the number 10 |

## Part (b)

| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| Attempt to rank number of pages (at least 4 correct) | M1 | Allow reverse ranks |
| Attempt at $d^2$ row (may be implied by $\sum d^2 = 66$ or $264$ for reverse ranks) | M1 | — |
| $r_s = 1 - \dfrac{6 \times 66}{10(100-1)}, [= 1 - 0.4] = 0.6$ | M1, A1 | For use of correct formula, follow through their $\sum d^2$ if clearly stated; A1 for $0.6$ (or $-0.6$ for reverse ranks) |

## Part (c)

| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $H_0: \rho = 0 \quad H_1: \rho > 0$ | B1 | Both hypotheses in terms of $\rho$, one tail $H_1$; hypotheses in words only (e.g. "no correlation") scores B0 |
| Critical value is $0.5636$ | B1 | If two-tailed $H_1$, allow cv $= 0.6485$ |
| $0.6 >$ cv so significant result and sufficient evidence to reject $H_0$; there is support for the librarian's belief, or there is evidence of a correlation between the number of pages in a book and the number of times it is borrowed | B1ft | Must mention "librarian" (or "he") or "number of pages" and "borrowing"; follow through their $r_s$ and cv (provided $|\text{cv}| < 1$) |