| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Two-sample z-test large samples |
| Difficulty | Standard +0.3 This is a standard two-sample t-test (or z-test given large samples) with clearly defined data and straightforward hypotheses. It requires routine application of hypothesis testing procedures taught in S3, with no conceptual complications or novel problem-solving—slightly easier than average due to its textbook nature, but the 8 marks reflect the need for complete working including hypotheses, test statistic calculation, critical value comparison, and conclusion in context. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Number of Students | Mean | Standard Deviation | |
| In a School Team | 50 | 32.8 s | 4.6 s |
| Not in a Team | 190 | 35.1 s | 8.0 s |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0 : \mu_A = \mu_Y\) \(\quad\) \(H_1 : \mu_A < \mu_Y\) | B1 | |
| 5% level \(\therefore\) C.R. is \(z < \text{−}1.6449\) | B1 | |
| test statistic \(= \frac{32.8−33.1}{\sqrt{\frac{4.2^2}{50}+\frac{4.6^2}{190}}} = \text{−}2.6382\) | M2 A2 | |
| in C.R. \(\therefore\) reject \(H_0\) | M1 | |
| there is evidence that those in school teams complete task quicker | A1 | (8) |
$H_0 : \mu_A = \mu_Y$ $\quad$ $H_1 : \mu_A < \mu_Y$ | B1 |
5% level $\therefore$ C.R. is $z < \text{−}1.6449$ | B1 |
test statistic $= \frac{32.8−33.1}{\sqrt{\frac{4.2^2}{50}+\frac{4.6^2}{190}}} = \text{−}2.6382$ | M2 A2 |
in C.R. $\therefore$ reject $H_0$ | M1 |
there is evidence that those in school teams complete task quicker | A1 | (8)For a project, a student is investigating whether more athletic individuals have better hand-eye coordination. He records the time it takes a number of students to complete a task testing coordination skills and notes whether or not they play for a school sports team. His results are as follows:
\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
& Number of Students & Mean & Standard Deviation \\
\hline
In a School Team & 50 & 32.8 s & 4.6 s \\
\hline
Not in a Team & 190 & 35.1 s & 8.0 s \\
\hline
\end{tabular}
\end{center}
Stating your hypotheses clearly, test at the 5\% level of significance whether or not there is evidence that those who play in a school team complete the task more quickly on average. [8 marks]
\hfill \mbox{\textit{Edexcel S3 Q5 [8]}}