F-test for equality of variances

A question is this type if and only if it involves testing whether two population variances are equal using the F-distribution, typically comparing two independent samples from normal populations.

4 questions · Standard +0.5

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Edexcel S4 2004 June Q1
4 marks Standard +0.8
  1. The random variable \(X\) has an \(F\)-distribution with 8 and 12 degrees of freedom.
Find \(\mathrm { P } \left( \frac { 1 } { 5.67 } < X < 2.85 \right)\).
(4)
Edexcel S4 2005 June Q1
6 marks Moderate -0.5
  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)
Edexcel S4 2011 June Q1
2 marks Challenging +1.2
  1. Find the value of the constant \(a\) such that
  2. Find the value of the constant \(a\) such that
$$\mathrm { P } \left( a < F _ { 8,10 } < 3.07 \right) = 0.94$$
Edexcel S4 2013 June Q1
4 marks Standard +0.3
  1. (a) Find the value of the constant \(a\) such that
$$\mathrm { P } \left( 1.690 < \chi _ { 7 } ^ { 2 } < a \right) = 0.95$$ The random variable \(Y\) follows an \(F\)-distribution with 6 and 4 degrees of freedom.
(b) (i) Find the upper \(1 \%\) critical value for \(Y\).
(ii) Find the lower \(1 \%\) critical value for \(Y\).