Moderate -0.8 This is a straightforward application of a known variance confidence interval formula for a normal distribution. Students need only recall the formula, look up z₀.₀₁ = 2.326, and compute 401.8 ± 2.326(4.1/√11). No problem-solving or conceptual insight required—pure routine calculation.
3 The masses of tins of a particular brand of spaghetti are normally distributed with mean \(\mu\) grams and standard deviation 4.1 grams.
A random sample of 11 tins of spaghetti has a mean mass of 401.8 grams.
Construct a \(98 \%\) confidence interval for \(\mu\), giving your values to one decimal place.
AWRT \(2.33\); condone \(2.32\); PI by a correct upper or lower limit of the confidence interval
\(401.8 \pm 2.33 \times \dfrac{4.1}{\sqrt{11}}\)
M1
Uses formula for upper or lower limit of a confidence interval using their \(z\)-value or \(t\)-value; condone use of \(\sqrt{4.1}\); PI
\(= (398.9,\ 404.7)\)
A1
Obtains correct confidence interval AWRT 1 d.p.; condone use of truncated \(z\)-value of \(2.32\)
Question total: 3 marks
## Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| $z = 2.33$ | B1 | AWRT $2.33$; condone $2.32$; PI by a correct upper or lower limit of the confidence interval |
| $401.8 \pm 2.33 \times \dfrac{4.1}{\sqrt{11}}$ | M1 | Uses formula for upper or lower limit of a confidence interval using their $z$-value or $t$-value; condone use of $\sqrt{4.1}$; PI |
| $= (398.9,\ 404.7)$ | A1 | Obtains correct confidence interval AWRT 1 d.p.; condone use of truncated $z$-value of $2.32$ |
**Question total: 3 marks**
3 The masses of tins of a particular brand of spaghetti are normally distributed with mean $\mu$ grams and standard deviation 4.1 grams.
A random sample of 11 tins of spaghetti has a mean mass of 401.8 grams.\\
Construct a $98 \%$ confidence interval for $\mu$, giving your values to one decimal place.\\
\hfill \mbox{\textit{AQA Further Paper 3 Statistics 2023 Q3 [3]}}