| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2011 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | F-test for equality of variances |
| Difficulty | Challenging +1.2 This question requires understanding of F-distribution tables and symmetry properties to find a critical value given a probability. While it involves the less common F-distribution (not chi-squared as stated in the topic), it's primarily a table lookup exercise with one conceptual step about tail probabilities. More challenging than routine single-tail lookups but still a standard S4 exercise. |
| Spec | 2.04h Select appropriate distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(F_{8,10} > 3.07) = 0.05\), so need \(P(F_{10,8} > x) = 0.01\), so \(x = 5.81\) | B1 | awrt 0.172 |
| \(a = \frac{1}{5.81} = \mathbf{0.172}\) | B1 | |
| Total: 2 marks |
# Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(F_{8,10} > 3.07) = 0.05$, so need $P(F_{10,8} > x) = 0.01$, so $x = 5.81$ | B1 | awrt 0.172 |
| $a = \frac{1}{5.81} = \mathbf{0.172}$ | B1 | |
| **Total: 2 marks** | | |
---\begin{enumerate}
\item Find the value of the constant $a$ such that
\item Find the value of the constant $a$ such that
\end{enumerate}
$$\mathrm { P } \left( a < F _ { 8,10 } < 3.07 \right) = 0.94$$
\hfill \mbox{\textit{Edexcel S4 2011 Q1 [2]}}