Does the probability of rejecting a true null hypothesis increases as the sample size increases?
as the sample size increases the standard error decreases and a smaller and smaller difference from the null mean becomes statistically significant. as the sample size increases to a very large number we do have a higher probability of committing a Type I Error. For example, if you have a null mean of 45 and standard deviation of 3.5, and you have a sample size of 50 with a sample mean of 44.5 we will not reject the null. however, if the sample size is 500 and the sample mean is 44.5 we would reject the null. overall it is a balancing act. as the sample size increase the mean will approach the mean of the population and you are more likely to have a representative sample, but as the standard deviation goes to zero any minor difference from the null will be statistically significant.
