| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a standard paired t-test question from S4 with straightforward application of a well-practiced procedure. Parts (a), (b), and (d) require recall of statistical concepts, while part (c) involves routine calculation of differences, test statistic, and comparison with critical values. The question is slightly easier than average because it follows a textbook template with no unusual features or interpretation challenges. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Car | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) |
| Emissions without device | 151.4 | 164.3 | 168.5 | 148.2 | 139.4 | 151.2 |
| Emissions with device | 148.9 | 162.7 | 166.9 | 150.1 | 140.0 | 146.7 |
An emission-control device is tested to see if it reduces CO$_2$ emissions from cars. The emissions from 6 randomly selected cars are measured with and without the device. The results are as follows.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Car & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ \\
\hline
Emissions without device & 151.4 & 164.3 & 168.5 & 148.2 & 139.4 & 151.2 \\
\hline
Emissions with device & 148.9 & 162.7 & 166.9 & 150.1 & 140.0 & 146.7 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item State an assumption that needs to be made in order to carry out a $t$-test in this case.
[1]
\item State why a paired $t$-test is suitable for use with these data.
[1]
\item Using a 5\% level of significance, test whether or not there is evidence that the device reduces CO$_2$ emissions from cars.
[8]
\item Explain, in context, what a type II error would be in this case.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q2 [12]}}