Pooled variance from two samples

A question is this type if and only if it asks the student to combine sample statistics from two groups (e.g. using Sxx values or given sample variances) to produce a single pooled or combined variance estimate for use in a subsequent test.

1 questions · Standard +0.8

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Edexcel S4 2011 June Q2
5 marks Standard +0.8
  1. Two independent random samples \(X _ { 1 } , X _ { 2 } , \ldots , X _ { 7 }\) and \(Y _ { 1 } , Y _ { 2 } , Y _ { 3 } , Y _ { 4 }\) were taken from different normal populations with a common standard deviation \(\sigma\). The following sample statistics were calculated.
$$s _ { x } = 14.67 \quad s _ { y } = 12.07$$ Find the \(99 \%\) confidence interval for \(\sigma ^ { 2 }\) based on these two samples.