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I clearly don't believe that there were 230k new farm jobs, after looking at the statistically significant description that they used in their own survey 230k is easily accounted for in their 90% probability of being within 290k of the number.
The 230k number is bogus because you were using inconsistent data. You should not believe it because it is wrong, not because of the accuracy of the survey.
However that still leaves the question of why there was such a large increase in the total Not in Labor Force Statistic.
Not really. If you have no faith in the accuracy of the unemployment data, you should have the same reservations about the Not In Labor Force data.