Is the experimental evidence pointing to the fact that we inhabit a supervoid sufficiently strong? In case it were a likely scenario, could this fact have any effect on the consensus value of the Hubble parameter at present time? And on the acceleration parameter? The reasons behind these crazy questions are: Could the local (in our supervoid) Cepheid I standard candels have a significant redshift due to a weak local gravitational pull inside the void and a strong one outside it? Could this non-expansion related redshifts be significant and introduce errors in the measurement of more distant galaxies redshifts?