I calculate the ratio between points per game at home and points per
game away. I want to prove that this ratio for one team is
significantly different from the population.
Taking this as what you want to do. That is, 1) use the total points from all games, and not use each game as a separate observation for that team. 2) Use Home points / Total points as the relevant metric. And, 3) compare this for one team to the population value.
A simple way would be to calculate a confidence interval for the binomial proportion of Home points / Total points. If this confidence interval doesn't contain the proportion for the population, then this team is significantly different than the population.
Here, 0.56 is outside the confidence interval, suggest the team is different from the population.
Home.points = 100
Total.points = 150
Population.prop = 0.56
### 95 percent confidence interval:
### 0.5851570 0.7414436
Another way to do essentially the same thing is use a binomial test using the the population proportion as the theoretical proportion. A significant p-value suggests that the team is different than the population.
Here, the p-value < 0.05, suggest the team is different from the population.
binom.test(Home.points, Total.points, Population.prop)
### number of successes = 100, number of trials = 150, p-value = 0.008429
### alternative hypothesis: true probability of success is not equal to 0.56