| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2004 |
| Session | June |
| Marks | 8 |
| 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 known variances, requiring straightforward application of the test procedure (hypotheses, test statistic calculation, critical value comparison). The only mild complexity is combining two samples, but the method is routine for S3. Slightly easier than average due to clear setup and standard procedure. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
3. It is known from past evidence that the weight of coffee dispensed into jars by machine $A$ is normally distributed with mean $\mu _ { \mathrm { A } }$ and standard deviation 2.5 g . Machine $B$ is known to dispense the same nominal weight of coffee into jars with mean $\mu _ { B }$ and standard deviation 2.3 g . A random sample of 10 jars filled by machine $A$ contained a mean weight of 249 g of coffee. A random sample of 15 jars filled by machine $B$ contained a mean weight of 251 g .
\begin{enumerate}[label=(\alph*)]
\item Test, at the $5 \%$ level of significance, whether or not there is evidence that the population mean weight dispensed by machine B is greater than that of machine A .
\item Write down an assumption needed to carry out this test.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2004 Q3 [8]}}