A plant geneticist has two pure breeding lines, one with purple petals and one with blue petals. She hypothesizes that the phenotypic difference is due to two alleles of one gene. To test this idea, she aims to look for a 3:1 ratio in the F2. She crosses the parental lines and finds that all of the F1 progeny are purple. The F1 plants are self-fertilized and 400 F2 plants are obtained. Of these, 320 are purple and 80 are blue. Required:
Use the chi-squared test to determine if these results support her hypothesis.