The unexpected dimness of Type Ia supernovae at redshifts z ≲ 1 has over the past 7 years been seen as an indication that the expansion of the universe is accelerating. A new model cosmology, the “fractal bubble model”, has been proposed by one of us, based on the idea that our observed universe resides in an underdense bubble remnant from a primordial epoch of cosmic inflation, together with a new solution for averaging in an inhomogeneous universe. Although there is no cosmic acceleration, it is claimed that the luminosity distance of type Ia supernovae data will nonetheless fit the new model, since it mimics a Milne universe at low redshifts. In this paper the hypothesis is tested statistically against the available type Ia supernovae data by both chi–square and Bayesian methods. While the standard model with cosmological constant ΩΛ = 1−Ωm is favoured by a Bayesian analysis with wide priors, the comparison depends strongly on the priors chosen for the density parameter, Ωm. The fractal bubble model gives better agreement generally for Ωm < 0.2. It also gives reasonably good fits for all the range, Ωm = 0.01–0.55, allowing the possibility of a viable cosmology with just baryonic matter, or alternatively with both baryonic matter and additional cold dark matter.