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Is the median of the F-distribution with m and n degrees of freedom decreasing in n, for any m?

From experiments it looks like it might be, but I have been unable to prove it.

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    Is n the denominator degrees of freedom?2012-09-25
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    @Michael yes it is2012-09-25
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    Have you looked at tables of the F distribution. I don't think the tables give percentiles close to 50 but maybe looking at the 25th and the 75th with a gross interpolation would give you an idea whether or not it is true. I am sure that there are software packages that will give the cumulative F or its inverse and you can see the result from that.2012-09-26
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    @Michael yes from software calculation it seems like the result is true. But I am looking for a proof!2012-09-27
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    If it is not true the tables could tell you by giving you just one counterexample. If you need precision you can do numerical integration to a desired level of accuracy.2012-09-27

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