| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2006 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test two variances hypothesis |
| Difficulty | Challenging +1.2 This is a Further Maths S4 question requiring chi-squared confidence intervals and an F-test for variance comparison. While the topic is advanced (Further Maths), the execution is straightforward: calculate sample variance from raw data, apply standard chi-squared formulas, then perform a routine F-test with clearly defined hypotheses. The calculations are mechanical with no conceptual traps or novel problem-solving required. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
2. The weights, in grams, of apples are assumed to follow a normal distribution.
The weights of apples sold by a supermarket have variance $\sigma _ { s } { } ^ { 2 }$. A random sample of 4 apples from the supermarket had weights
$$\text { 114, 100, 119, } 123 .$$
\begin{enumerate}[label=(\alph*)]
\item Find a 95\% confidence interval for $\sigma _ { s } ^ { 2 }$.
The weights of apples sold on a market stall have variance $\sigma _ { M } ^ { 2 }$. A second random sample of 7 apples was taken from the market stall. The sample variance $s _ { M } ^ { 2 }$ of the apples was 318.8.
\item Stating your hypotheses clearly test, at the $1 \%$ levcel of significnace, whether or not there is evidence that $\sigma _ { M } ^ { 2 } > \sigma _ { s } ^ { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 2006 Q2 [12]}}