# Question 7:

## Part (a): Mean and Standard Deviation [4 marks]

| Answer/Working | Mark | Guidance |
|---|---|---|
| Midpoints used: 37.5, 42.5, 47.5, 52.5, 57.5, 62.5, 67.5, 72.5, 77.5, 82.5, 87.5, 92.5, 97.5 | B1 | At least one midpoint correct |
| $\sum fx = 4(37.5) + 9(42.5) + 12(47.5) + 16(52.5) + 24(57.5) + 28(62.5) + 24(67.5) + 17(72.5) + 12(77.5) + 7(82.5) + 4(87.5) + 2(92.5) + 1(97.5) = 10056$ | M1 | Attempt at $\sum fx$ |
| $\bar{x} = \frac{10056}{160} = 62.85$ | A1 | Correct mean |
| $s = \sqrt{\frac{\sum fx^2}{160} - \bar{x}^2} = \sqrt{\frac{659827.5}{160} - 62.85^2} = \sqrt{4123.92 - 3950.12} \approx 13.18$ | A1 | Correct standard deviation (accept values in range 13.1–13.2) |

## Part (b)(i): 98% Confidence Interval [5 marks]

| Answer/Working | Mark | Guidance |
|---|---|---|
| $z = 2.3263$ for 98% CI | B1 | Correct $z$ value |
| $SE = \frac{s}{\sqrt{n}} = \frac{13.18}{\sqrt{160}}$ | M1 | Correct standard error structure |
| $= 1.0424...$ | A1 | Correct SE value |
| $CI: \bar{x} \pm z \times SE = 62.85 \pm 2.3263 \times 1.0424$ | M1 | Correct CI structure |
| $(60.43, 65.27)$ | A1 | Correct interval (follow through on values) |

## Part (b)(ii): Comment on Claim [2 marks]

| Answer/Working | Mark | Guidance |
|---|---|---|
| 61.7 lies within the confidence interval $(60.43, 65.27)$ | M1 | Comparison of 61.7 with CI |
| There is insufficient evidence to suggest the mean weight has increased from 61.7 kg; the claim is not supported at the 2% significance level | A1 | Correct conclusion in context |

These pages (27 and 28) are **answer space/blank pages** from an AQA exam paper (P/Jun14/SS1B). They contain:

- Page 27: Blank lined answer space for Question 7
- Page 28: A blank "do not write on this page" page

**There is no mark scheme content on these pages.** These are student answer booklet pages, not mark scheme pages. To extract mark scheme content, you would need to provide the actual mark scheme document for this paper.