| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test two variances hypothesis |
| Difficulty | Standard +0.3 This is a standard two-sample F-test for equality of variances with clearly given sample variances and sizes. It requires routine application of the F-test procedure (stating hypotheses, calculating F-statistic, finding critical values, conclusion) with no conceptual challenges or novel problem-solving. The question is slightly easier than average because all necessary values are provided and the procedure is algorithmic, though it does require knowledge of the F-distribution which is S4-specific content. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
A beach is divided into two areas $A$ and $B$. A random sample of pebbles is taken from each of the two areas and the length of each pebble is measured. A sample of size 26 is taken from area $A$ and the unbiased estimate for the population variance is $s_A^2 = 0.495 \text{ mm}^2$. A sample of size 25 is taken from area $B$ and the unbiased estimate for the population variance is $s_B^2 = 1.04 \text{ mm}^2$.
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly test, at the 10\% significance level, whether or not there is a difference in variability of pebble length between area $A$ and area $B$. [5]
\item State the assumption you have made about the populations of pebble lengths in order to carry out this test. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q1 [6]}}