| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | F-test for equality of variances |
| Difficulty | Moderate -0.5 This is a straightforward table lookup question requiring no conceptual understanding or problem-solving. Part (a) involves reading chi-squared probabilities from tables, and part (b) requires finding F-distribution critical values from tables. While the topic is Further Maths S4, the question itself demands only mechanical table reading with no calculation or reasoning, making it easier than average A-level questions that typically require some problem-solving. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
\begin{enumerate}
\item The random variable $X$ has a $\chi ^ { 2 }$-distribution with 9 degrees of freedom.\\
(a) Find $\mathrm { P } ( 2.088 < X < 19.023 )$.
\end{enumerate}
The random variable $Y$ follows an $F$-distribution with 12 and 5 degrees of freedom.\\
(b) Find the upper and lower $5 \%$ critical values for $Y$.\\
(3)\\
(Total 6 marks)\\
\hfill \mbox{\textit{Edexcel S4 2005 Q1 [6]}}