<p>Some combinatorial statistics are introduced and counted in this paper, including the number of alternating ordered trees rooted at vertex 0, and the number of corresponding prime parking functions for a parking function. It is shown that the above-mentioned combinatorial statistics are equidistributed. More generally, more equidistributed statistics could be established in an analogous way, which are supplements of the four equidistributed statistics found by Duarte and Oliveira in [The number of parking functions with center of a given length, Adv. Appl. Math. 107 (2019) 125–143]. Some combinatorial properties of these equidistributed statistics are also obtained. As another application, we give combinatorial proofs and refined version of two hook length formulas for plane trees and plane forests, obtained by Chen, Gao, and Guo [Hook length formulas for trees by Han’s Expansion, Electron. J. Combin. 16 (2009) #P62].</p>