| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test then t-test sequential |
| Difficulty | Standard +0.8 This is a standard S4 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 interpretation of the grocer's belief (requiring a one-tailed test with H₀: μ_B - μ_A ≥ 150), these are well-practiced procedures in S4. The question is methodical rather than conceptually challenging, placing it moderately above average difficulty for A-level but routine for Further Maths Statistics students. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
A grocer receives deliveries of cauliflowers from two different growers, $A$ and $B$. The grocer takes random samples of cauliflowers from those supplied by each grower. He measures the weight $x$, in grams, of each cauliflower. The results are summarised in the table below.
\includegraphics{figure_7}
\begin{enumerate}[label=(\alph*)]
\item Show, at the 10\% significance level, that the variances of the populations from which the samples are drawn can be assumed to be equal by testing the hypothesis H₀: $\sigma_A^2 = \sigma_B^2$ against hypothesis H₁: $\sigma_A^2 \neq \sigma_B^2$.
(You may assume that the two samples come from normal populations.) [6]
\end{enumerate}
The grocer believes that the mean weight of cauliflowers provided by $B$ is at least 150 g more than the mean weight of cauliflowers provided by $A$.
\begin{enumerate}[label=(\alph*)]
\item[(b)] Use a 5\% significance level to test the grocer's belief. [8]
\item Justify your choice of test. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q7 [16]}}