What is the effect of increasing sample size on the error rates in a hypothesis test?

Increasing the sample size decreases the chance of a Type II error but does not have any effect on the chance of a Type I error.

In the graph below (which hopefully illustrates this idea) we consider spinning a coin n times to determine whether the coin is biased. The red shaded region corresponds with the chance of a Type I error and the green shaded region corresponds with the chance of a Type II error if the true chance of heads is .60.

Animations that display this:

n=100 -> n=500 then repeat
n=100 -> n=500 and back