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We apply a recently developed theoretical model of helium emission toobservations of both the Orion Nebula and a sample of extragalactic H IIregions. In the Orion analysis, we eliminate some weak and blended lines andcompare theory and observation for our reduced line list. With our besttheoretical model we find an average difference between theoretical andobserved intensities $<I_{predicted}/I_{observed}-1> = 6.5%$. We argue thatboth the red and blue ends of the spectrum may have been inadequately correctedfor reddening. For the 22 highest quality lines, with $3499{\AA}\le\lambda\le6678 {\AA}$, our best model predicts observations to anaverage of 3.8%. We also perform an analysis of the reported observationalerrors and conclude they have been underestimated. In the extragalacticanalysis, we demonstrate the likelihood of a large systematic error in thereported data and discuss possible causes. This systematic error is at least aslarge as the errors associated with nearly all attempts to calculate theprimordial helium abundance from such observations. Our Orion analysis suggeststhat the problem does not lie in the theoretical models. We demonstrate acorrelation between equivalent width and apparent helium abundance of linesfrom extragalactic sources that is most likely due to underlying stellarabsorption. Finally, we present fits to collisionless case-B He I emissivitiesas well as the relative contributions due to collisional excitations out of themetastable $2s {}^{3}S$ term.Comment: accepted for publication in Ap

HeiEmission in the Orion Nebula and Implications for Primordial Helium Abundance