| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2008 |
| Session | June |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test then t-test sequential |
| Difficulty | Standard +0.3 This is a standard two-sample hypothesis testing question requiring an F-test for variances followed by a t-test for means. While it involves multiple parts and requires careful calculation of sample statistics, it follows a completely routine procedure taught in S4 with no novel problem-solving or conceptual challenges—students simply apply memorized tests with given significance levels. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
| Sample from Group \(A\) | 42 | 40 | 35 | 37 | 34 | 43 | 42 | 44 | 49 |
| Sample from Group \(B\) | 40 | 44 | 38 | 47 | 38 | 37 | 33 |
\begin{enumerate}
\item A large number of students are split into two groups $A$ and $B$. The students sit the same test but under different conditions. Group A has music playing in the room during the test, and group B has no music playing during the test. Small samples are then taken from each group and their marks recorded. The marks are normally distributed.
\end{enumerate}
The marks are as follows:
\begin{center}
\begin{tabular}{ l l l l l l l l l l }
Sample from Group $A$ & 42 & 40 & 35 & 37 & 34 & 43 & 42 & 44 & 49 \\
Sample from Group $B$ & 40 & 44 & 38 & 47 & 38 & 37 & 33 & & \\
\end{tabular}
\end{center}
(a) Stating your hypotheses clearly, and using a $10 \%$ level of significance, test whether or not there is evidence of a difference between the variances of the marks of the two groups.\\
(b) State clearly an assumption you have made to enable you to carry out the test in part (a).\\
(c) Use a two tailed test, with a $5 \%$ level of significance, to determine if the playing of music during the test has made any difference in the mean marks of the two groups. State your hypotheses clearly.\\
(d) Write down what you can conclude about the effect of music on a student's performance during the test.
\hfill \mbox{\textit{Edexcel S4 2008 Q2 [17]}}