Final answer:
The null hypotheses for testing sex differences in gait velocity among three age groups involve no significant difference between sexes and no significant difference across age groups for this velocity. Additionally, the null for the interaction effect is that there is no interaction between sex and age group concerning gait velocity.
Step-by-step explanation:
The goal is to test for sex differences in gait velocity among three age groups. The null hypothesis for each main effect and the interaction can be formulated based on factorial ANOVA principles.
Null Hypotheses for Main Effects
- Sex: There is no significant difference in gait velocity between sexes.
- Age Group: There is no significant difference in gait velocity across the three age groups.
Null Hypothesis for Interaction Effect
The interaction effect's null hypothesis would be that there is no interaction between sex and age group in terms of gait velocity, implying that any differences across age groups are consistent between sexes.