| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Two-sample t-test with summary statistics |
| Difficulty | Standard +0.3 This is a straightforward two-sample z-test with large samples (n₁=100, n₂=80) where students apply a standard procedure: state hypotheses, calculate test statistic using given means and standard deviations, compare to critical value at 1% level, and conclude. The question is slightly easier than average because it's a routine application of a standard test with all values provided and clear instructions, though it requires careful calculation and proper hypothesis statement. |
| 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 80 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 Q2 [9]}}