| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test then t-test sequential |
| Difficulty | Standard +0.3 This is a standard two-sample hypothesis testing question requiring an F-test for variance equality followed by a two-sample t-test for means. While it involves multiple steps and careful hypothesis statement, both procedures are routine S4 content with straightforward application of formulas and critical value lookups. The question is slightly easier than average because it explicitly guides students through the logical sequence (test variances first, then means) and requires no conceptual insight beyond textbook procedures. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
The lengths, $x$ mm, of the forewings of a random sample of male and female adult butterflies are measured. The following statistics are obtained from the data.
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Assuming the lengths of the forewings are normally distributed test, at the 10\% level of significance, whether or not the variances of the two distributions are the same. State your hypotheses clearly. [7]
\item Stating your hypotheses clearly test, at the 5\% level of significance, whether the mean length of the forewings of the female butterflies is less than the mean length of the forewings of the male butterflies. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q3 [13]}}