Edexcel S4 2005 June — Question 1 6 marks

Exam BoardEdexcel
ModuleS4 (Statistics 4)
Year2005
SessionJune
Marks6
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Mark schemeDownload PDF ↗
TopicChi-squared goodness of fit
TypeF-test for equality of variances
DifficultyModerate -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.
Spec5.05c Hypothesis test: normal distribution for population mean

  1. The random variable \(X\) has a \(\chi ^ { 2 }\)-distribution with 9 degrees of freedom.
    1. Find \(\mathrm { P } ( 2.088 < X < 19.023 )\).
    The random variable \(Y\) follows an \(F\)-distribution with 12 and 5 degrees of freedom.
  2. Find the upper and lower \(5 \%\) critical values for \(Y\).
    (3)
    (Total 6 marks)

\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]}}