OMB Meeting Book - January 8, 2015

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95% confidence interval for Sigma, given normal distribution

Degrees of

LCL

UCL Multiplier

Freedom Multiplier Multiplier

Ratio 1 0.446 31.910 71.52 2 0.521 6.285 12.07 3 0.566 3.729 6.58 4 0.599 2.874 4.80 5 0.624 2.453

3.93 <-- Long considered the minimum d.f. needed to estimate Sigma

6 0.644 2.202 7 0.661 2.035 8 0.675 1.916 9 0.688 1.826 10 0.699 1.755 12 0.717 1.651 15 0.739 1.548 18 0.756 1.479 20 0.765 1.444 25 0.784 1.380 30 0.799 1.337 35 0.811 1.304

3.42

3.08 <-- Rough 'knee' of the multiplier ratio curve

2.84 2.65 2.51 2.30 2.10 1.96 1.89 1.76 1.67 1.61

100

10

1

0

5

10

15

20

25

30

35

0

Degrees of Freedom

LCL Multiplier

UCL Multiplier

Multiplier Ratio

2

Recommended to OMB by Committee on Statistics: 07-17-2013 Reviewed and approved by OMB: 07-18-2013 by Committee on S atistics: 07-17-2 13

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