Standard +0.3 This is a straightforward application of the t-distribution confidence interval formula with given summary statistics. Students need to calculate the sample standard deviation, find the critical t-value for 7 degrees of freedom, and apply the standard formula. While it requires knowledge of the t-distribution (a Further Maths topic), the execution is mechanical with no problem-solving or conceptual challenges beyond routine application.
1 The times taken by members of a large quiz club to complete a challenge have a normal distribution with mean \(\mu\) minutes. The times, \(x\) minutes, are recorded for a random sample of 8 members of the club. The results are summarised as follows, where \(\bar { x }\) is the sample mean.
$$\bar { x } = 33.8 \quad \sum ( x - \bar { x } ) ^ { 2 } = 94.5$$
Find a 95\% confidence interval for \(\mu\).
1 The times taken by members of a large quiz club to complete a challenge have a normal distribution with mean $\mu$ minutes. The times, $x$ minutes, are recorded for a random sample of 8 members of the club. The results are summarised as follows, where $\bar { x }$ is the sample mean.
$$\bar { x } = 33.8 \quad \sum ( x - \bar { x } ) ^ { 2 } = 94.5$$
Find a 95\% confidence interval for $\mu$.\\
\hfill \mbox{\textit{CAIE Further Paper 4 2022 Q1 [4]}}