| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Two-sample t-test equal variance |
| Difficulty | Standard +0.3 This is a standard two-sample inference question from S4 requiring an F-test for equality of variances and a confidence interval for difference in means. While it involves multiple steps and careful attention to pooled vs unpooled procedures, these are routine textbook techniques with no novel problem-solving required. The conceptual demand is moderate for A-level statistics, making it slightly easier than average overall. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
| Sample size \(n\) | Standard deviation \(s\) | Mean \(\bar{x}\) | |
| With background music | 8 | 4.1 | 15.9 |
| Without background music | 7 | 5.2 | 17.9 |
A teacher wishes to test whether playing background music enables students to complete a task more quickly. The same task was completed by 15 students, divided at random into two groups. The first group had background music playing during the task and the second group had no background music playing.
The times taken, in minutes, to complete the task are summarised below.
\begin{tabular}{|c|c|c|c|}
\hline
& Sample size $n$ & Standard deviation $s$ & Mean $\bar{x}$ \\
\hline
With background music & 8 & 4.1 & 15.9 \\
\hline
Without background music & 7 & 5.2 & 17.9 \\
\hline
\end{tabular}
You may assume that the times taken to complete the task by the students are two independent random samples from normal distributions.
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly, test, at the 10\% level of significance, whether or not the variances of the times taken to complete the task with and without background music are equal.
[5]
\item Find a 99\% confidence interval for the difference in the mean times taken to complete the task with and without background music.
[7]
\end{enumerate}
Experiments like this are often performed using the same people in each group.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Explain why this would not be appropriate in this case.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q1 [13]}}