Standard +0.3 This is a straightforward confidence interval construction for a normal distribution mean with small sample size. Students need to calculate the sample mean, use the t-distribution (since n=10 is small), and apply the standard formula. While it requires knowing when to use t vs z and careful arithmetic, it's a routine S2 procedure with no conceptual challenges beyond standard bookwork.
The error, \(X\) °C, made in measuring a patient's temperature at a local doctors' surgery may be modelled by a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).
The errors, \(x\) °C, made in measuring the temperature of each of a random sample of \(10\) patients are summarised below.
$$\sum x = 0.35 \quad \text{and} \quad \sum(x - \bar{x})^2 = 0.12705$$
Construct a \(99\%\) confidence interval for \(\mu\), giving the limits to three decimal places. [5 marks]
The error, $X$ °C, made in measuring a patient's temperature at a local doctors' surgery may be modelled by a normal distribution with mean $\mu$ and standard deviation $\sigma$.
The errors, $x$ °C, made in measuring the temperature of each of a random sample of $10$ patients are summarised below.
$$\sum x = 0.35 \quad \text{and} \quad \sum(x - \bar{x})^2 = 0.12705$$
Construct a $99\%$ confidence interval for $\mu$, giving the limits to three decimal places. [5 marks]
\hfill \mbox{\textit{AQA S2 2010 Q4 [5]}}