This note discusses three interconnected statistical problems concerning the Parkfield sequence of moderate earthquakes and the Parkfield prediction experiment: (a) Is it possible that the quasi-periodic Parkfield sequence of characteristic earthquakes is no uncommon, specific phenomenon (the research hypothesis), but can be explained by a preferential selection from available earthquake catalogs? To this end we formulate the null hypothesis (earthquakes occur according to the Poisson process in time and their size follows the Gutenberg-Richter relation). We test whether the null hypothesis can be rejected as an explanation for the Parkfield sequence. (b) If the null hypothesis cannot be refuted, what is the probability of magnitude m ≥ 6 earthquake occurrence in the Parkfield region? (c) The direct goal of the Parkfield experiment is the registration of precursory phenomena prior to a m6 earthquake. However, in the absence of the characteristic earthquake, can the experiment resolve which of the two competing hypotheses is true in a reasonable time? Statistical analysis is hindered by an insufficiently rigorous definition of the research model and inadequate or ambiguous data. However, we show that the null hypothesis cannot be decisively rejected. The quasi-periodic pattern of intermediate size earthquakes in the Parkfield area is a statistical event likely to occur by chance if it has been preferentially selected from available earthquake catalogs. The observed magnitude-frequency curves for small and intermediate earthquakes in the Parkfield area agree with the theoretical distribution computed on the basis of a modified Gutenberg-Richter law (gamma distribution), using deformation rates for the San Andreas fault. We show that the size distribution of the Parkfield characteristic earthquakes can also be attributed to selection bias. According to the null hypothesis, the yearly probability of a m ≥ 6 earthquake originating in the Parkfield area is less than 1%, signifying that several more decades of observation may be needed before the expected event occurs. By its design, the Parkfield experiment cannot be expected to yield statistically significant conclusions on the validity of the research hypothesis for many decades.