Context. Cosmic chronometers may be used to measure the age difference between passively evolving galaxy populations to calculate the Hubble parameter H(z) as a function of redshift z. The age estimator emerges from the relationship between the amplitude of the rest frame Balmer break at 4000 Å and the age of a galaxy, assuming that there is one single stellar population within each galaxy. Aims: First, we analyze the effect on the age estimates from the possible contamination (< 2.4% of the stellar mass in our high-redshift sample) of a young component of ≲ 100 Myr embedded within the predominantly old population of the quiescent galaxy. Recent literature has shown this combination to be present in very massive passively evolving galaxies. Second, we evaluate how the available data compare with the predictions of nine different cosmological models. Methods: For the first task, we calculated the average flux contamination due to a young component in the Balmer break from the data of 20 galaxies at z > 2 that included photometry from the far-ultraviolet to near-infrared at rest. For the second task, we compared the data with the predictions of each model, using a new approach of distinguishing between systematic and statistical errors. In previous work with cosmic chronometers, these have simply been added in quadrature. We also evaluated the effects of contamination by a young stellar component. Results: The ages inferred using cosmic chronometers represent a galaxy-wide average rather than a characteristic of the oldest population alone. The average contribution from the young component to the rest luminosity at 4000 Å may constitute a third of the luminosity in some samples, which means that this is far from negligible. This ratio is significantly dependent on stellar mass, proportional to M-07. Consequently, the measurements of the absolute value of the age or the differential age between different redshifts are at least partially incorrect and make the calculation of H(z) very inaccurate. Some cosmological models, such as the Einstein-de Sitter model or quasi-steady state cosmology, which are rejected under the assumption of a purely old population, can be made compatible with the predicted ages of the Universe as a function of redshift if we take this contamination into account. However, the static Universe models are rejected by these H(z) measurements, even when this contamination is taken into account.