| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a straightforward paired t-test application with clear before/after data. Students must calculate differences, find mean and standard deviation, then perform a one-tailed test—all standard S3 procedures requiring minimal problem-solving beyond routine execution of the test protocol. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
| Mark before fieldwork | 19 | 84 | 84 | 99 | 59 | 19 | 29 | 49 | 54 | 69 |
| Mark after fieldwork | 23 | 98 | 83 | 88 | 68 | 33 | 28 | 53 | 58 | 88 |
4 A group of students were tested in geography before and after a fieldwork course. The marks of 10 randomly selected students are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Student & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Mark before fieldwork & 19 & 84 & 84 & 99 & 59 & 19 & 29 & 49 & 54 & 69 \\
\hline
Mark after fieldwork & 23 & 98 & 83 & 88 & 68 & 33 & 28 & 53 & 58 & 88 \\
\hline
\end{tabular}
\end{center}
(i) Use a suitable $t$-test, at the $5 \%$ level of significance, to test whether the students' performance has improved.\\
(ii) State the necessary assumption in applying the test.
\hfill \mbox{\textit{OCR S3 2016 Q4 [9]}}