| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Pooled variance estimation |
| Difficulty | Standard +0.3 This is a standard two-sample t-test with pooled variance from S3, requiring routine application of a learned procedure. Students must state hypotheses, calculate pooled variance, compute the test statistic, and compare to critical value—all straightforward steps with clear data provided. Parts (b) and (c) test basic understanding of CLT and assumptions, which are standard bookwork. Slightly above average difficulty only because it's a multi-step hypothesis test rather than pure recall, but this is a textbook S3 question with no novel insight required. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05c Hypothesis test: normal distribution for population mean |
| Mean, \(\overline { \boldsymbol { t } }\) | Standard deviation, \(\boldsymbol { s }\) | \(\boldsymbol { n }\) | |
| Children | 61.2 | 5.9 | 60 |
| Adults | 59.1 | 5.2 | 50 |
4. A random sample of 60 children and a random sample of 50 adults were taken and each person was given the same task to complete.
The table below summarises the times taken, $t$ seconds, to complete the task.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& Mean, $\overline { \boldsymbol { t } }$ & Standard deviation, $\boldsymbol { s }$ & $\boldsymbol { n }$ \\
\hline
Children & 61.2 & 5.9 & 60 \\
\hline
Adults & 59.1 & 5.2 & 50 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly, test, at the $5 \%$ level of significance, whether or not there is evidence that the mean time taken to complete the task by children is greater than the mean time taken by adults.\\
(6)
\item Explain the relevance of the Central Limit Theorem to your calculation in part (a).
\item State an assumption you have made to carry out the test in part (a).
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2016 Q4 [8]}}