| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2002 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Two-sample t-test with summary statistics |
| Difficulty | Standard +0.3 This is a standard two-sample z-test with clearly stated data and a routine hypothesis test structure. While it requires multiple steps (stating hypotheses, calculating pooled standard error, computing test statistic, comparing to critical value), these are all textbook procedures with no conceptual challenges. The 8 marks reflect the working required rather than difficulty. Slightly above average only because it's a two-sample test rather than one-sample. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05c Hypothesis test: normal distribution for population mean |
A random sample of 100 classical CDs produced by a record company had a mean playing time of 70.6 minutes and a standard deviation of 9.1 minutes. An independent random sample of 120 CDs produced by a different company had a mean playing time of 67.2 minutes with a standard deviation of 8.4 minutes.
\begin{enumerate}[label=(\alph*)]
\item Using a 1\% level of significance, test whether or not there is a difference in the mean playing times of the CDs produced by these two companies. State your hypotheses clearly. [8]
\item State an assumption you made in carrying out the test in part (a). [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2002 Q2 [9]}}