Power analysis in statistics with R. There is a probability of committing an error in making a decision about a hypothesis. For testing null against alternative hypothesis, the test with probabilities a and b of type 1 and type 2 errors respectively, the quantity is called the power of test. It allows us to determine the sample size required to detect an effect of a given size with given degree of confidence.

I am conducting an experiment on the resting heart rates of children vs adults, with my hypothesis being the mean restin heart rates of children is higher than adults. I have conducted a two-sided t test with 100 samples: 50 children and 50 adults. The mean resting heart rates for adults is 81.06, and for children its 89.90.My professor wants us to calculate power, one time using the data we currently have, then to calculate power again, this time to find out what the ideal number ofcandidates would be good to run this experiment practically. This can be calculated by hand or by r, please show me how to do both, and the methodology.