Does the probability of rejecting a true null hypothesis increases as the sample size increases?

Does the probability of rejecting a true null hypothesis increases as the sample size increases?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.Does the probability of rejecting a true null hypothesis increases as the sample size increases?
As the second person notes, the smaller the sample the better chance of making a mistake and rejecting a true hypothesis. When one designs a study, one want to ';power'; the study as much as possible by increasing the sample size and increasing the chance of detecting a significant difference (decreasing ';beta';, the chance of rejecting a true hypothesis, the ';power'; is 1-beta) when there really is a difference (i.e. correctly rejecting the null hypothesis)
You need to review Type I and Type II errors.....





The following is true: smaller the sample, the more likely you are to commit a type II error
That would contradict logic altogether.





More data leads to more chance of a mistake? How strange.