A researcher crossed several randomly-chosen pink tree peonies, Paeonia suffruticosa, in order to test a genetic model of inheritance. She expected to see red:pink:white offspring colors in the ratio of 12:3:1. Below are the observed color proportions of the 83 plants in the study:

Observed Proportions of Progeny Colors
Red Pink White
0.747 0.205 0.048

Conduct a hypothesis test to determine if the observed proportions significantly differ from the expected ratio. Show all your work and include all steps including your assumptions.