The H ii galaxy Hubble diagram strongly favoursRh=ctover ΛCDM

We continue to build support for the proposal to use HII galaxies (HIIGx) and giant extragalactic HII regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. Using a sample of 25 high-redshift HIIGx, 107 local HIIGx, and 24 GEHR, we confirm that the correlation between the emission-line luminosity and ionized-gas velocity dispersion is a viable luminosity indicator, and use it to test and compare the standard model LCDM and the R_h=ct Universe by optimizing the parameters in each cosmology using a maximization of the likelihood function. For the flat LCDM model, the best fit is obtained with Omega_m=0.40_{-0.09}^{+0.09}. However, statistical tools, such as the Akaike (AIC), Kullback (KIC) and Bayes (BIC) Information Criteria favor R_h=ct over the standard model with a likelihood of ~94.8%-98.8% versus only ~1.2%-5.2%. For wCDM (the version of LCDM with a dark-energy equation of state w_de=p_de/rho_de rather than w_de=w_L=-1), a statistically acceptable fit is realized with Omega_m=0.22_{-0.14}^{+0.16} and w_de=-0.51_{-0.25}^{+0.15} which, however, are not fully consistent with their concordance values. In this case, wCDM has two more free parameters than R_h=ct, and is penalized more heavily by these criteria. We find that R_h=ct is strongly favored over wCDM with a likelihood of ~92.9%-99.6% versus only 0.4%-7.1%. The current HIIGx sample is already large enough for the BIC to rule out LCDM/wCDM in favor of R_h=ct at a confidence level approaching 3sigma.