How can type 1 and type 2 errors be minimized?
The probability of a type 1 error (rejecting a true null hypothesis) can be minimized by picking a smaller level of significance
Once the level of significance is set, the probability of a type 2 error (failing to reject a false null hypothesis) can be minimized either by picking a larger sample size or by choosing a "threshold" alternative value of the parameter in question that is further from the null value. This threshold alternative value is the value you assume about the parameter when computing the probability of a type 2 error.
To be "honest" from intellectual, practical, and perhaps moral perspectives, however, the threshold value should be picked based on the minimal "important" difference from the null value that you'd like to be able to correctly detect (if it's true). Therefore, the best thing to do is to increase the sample size.
The level of significance
Once a level of significance
By increasing the sample size, you reduce the variability of the statistic in question, which will reduce its chances of failing to be in the rejection region when its true sampling distribution would indicate that it should be in the rejection region.
By choosing a threshold value of the parameter (under which to compute the probability of a type 2 error) that is further from the null value, you reduce the chance that the test statistic will be close to the null value when its sampling distribution would indicate that it should be far from the null value (in the rejection region).
For example, suppose we are testing the null hypothesis