Output in China’s manufacturing sector contracted in the first three weeks of August at the fastest pace since the depths of the financial crisis, a survey released Friday showed. The survey, a preliminary reading of the Caixin purchasing managers’ index, came in at 47.1 points for August, compared with 47.8 points in July. The August figure was its lowest reading since March 2009 on a scale in which any figure below 50 indicates contraction.