| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2024 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Two-sample t-test (unknown variances) |
| Difficulty | Standard +0.3 This is a standard two-sample t-test with unequal variances following a routine procedure: state hypotheses, calculate pooled variance and test statistic, compare to critical value. While it requires careful calculation and knowledge of the correct test, it's a textbook application with no novel insight required. Slightly easier than average due to clear setup and straightforward interpretation. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.05c Hypothesis test: normal distribution for population mean |
| \(n\) | \(\bar { x }\) | \(s ^ { 2 }\) | |
| Undergraduates studying History | 38 | 56.3 | 27.2 |
| Undergraduates studying Maths | 45 | 39.8 | 18.5 |
\begin{enumerate}
\item A professor claims that undergraduates studying History have a typing speed of more than 15 words per minute faster than undergraduates studying Maths.
\end{enumerate}
A sample is taken of 38 undergraduates studying History and 45 undergraduates studying Maths. The typing speed, $x$ words per minute, of each undergraduate is recorded. The results are summarised in the table below.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& $n$ & $\bar { x }$ & $s ^ { 2 }$ \\
\hline
Undergraduates studying History & 38 & 56.3 & 27.2 \\
\hline
Undergraduates studying Maths & 45 & 39.8 & 18.5 \\
\hline
\end{tabular}
\end{center}
(a) Use a suitable test, at the $5 \%$ level of significance, to investigate the professor's claim.\\
State clearly your hypotheses, test statistic and critical value.\\
(b) State two assumptions you have made in carrying out the test in part (a).
\hfill \mbox{\textit{Edexcel S3 2024 Q5 [9]}}