# Question 7:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Label full time staff 1–6000, part time staff 1–4000 | M1 | One set of correct numbers |
| Use random numbers to select | M1 | |
| Simple random sample of 120 full time and 80 part time staff | A1 | |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Enables estimation of statistics/errors for each strata, or "reduce variability", or "more representative", or "reflects population structure" | B1 | NOT "more accurate" |

## Part (c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \mu_f = \mu_p,\quad H_1: \mu_f \neq \mu_p$ (accept $\mu_1, \mu_2$) | B1 | |
| $\text{s.e.} = \sqrt{\frac{21}{80} + \frac{19}{80}}$ | M1 | For attempt at s.e.; condone one number wrong; correct s.e. $= \sqrt{\frac{1}{2}}$ |
| $z = \frac{52 - 50}{\sqrt{\frac{21}{80} + \frac{19}{80}}} = (2\sqrt{2})$ | M1 | Must be $\frac{\pm(52-50)}{\sqrt{\frac{p}{q}+\frac{r}{s}}}$ |
| $= 2.828...$ awrt **2.83** | A1 | |
| Two tailed cv: $z = 2.5758$ (or prob awrt 0.002 or 0.004) | B1 | |
| $[2.828 > 2.5758]$ significant, reject $H_0$ | dM1 | Dependent on 2nd M1 |
| Evidence of difference in policy awareness between full time and part time staff | A1ft | Must mention "scores"/"policy awareness" and types of staff; A0 for one-tailed comment |

## Part (d):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Can use mean full time and mean part time | B1 | Mention of mean(s) or use of $\bar{X}$ (clearly referring to full-time or part-time) |
| $\sim$ Normal | B1 | Distribution can be assumed normal |

## Part (e):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Have assumed $s^2 = \sigma^2$ or variance of sample $=$ variance of population | B1 | |

## Part (f):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $2.53 < 2.5758$, not significant or do not reject $H_0$ | M1 | |
| Insufficient evidence of a difference in mean awareness | A1ft | Accept "no difference in mean scores"; allow ft |

## Part (g):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Training course has closed the gap between full time and part time staff's mean awareness of company policy | B1 | Must imply training was effective; supported by (c) and (f); condone one-tailed comment here |