How to plot mean line of multiple lines using ggplot?

Question

I am working through an example creating a faceted plot using ggplot. The plot contains 4 subplots, each with multiple lines. How do you plot the mean line for each of the subplots? My attempt is shown below:

library(datasets)
data(ChickWeight)

library(ggplot2)
g = ggplot(ChickWeight, aes(x = Time, y = weight))
g = g + geom_line(aes(group = Chick, color = Diet))
g = g + facet_grid(. ~ Diet)
g = g + stat_summary(aes(group = Diet), fun.y=mean, size = 1, color="black", geom="line")
g

I am unsure if I am using the geom_summary function correctly. I also tried geom_smooth(method = "lm", se = FALSE) but was unsure whether this output was the same as the mean.