Type I error and Type II error
Power of a test
Power of a test is given by 1 – probability (Type II error). In other words it is the probability of rejecting the null when it is false. When more than one test statistic can be used, power of a test helps in deciding which one is to be used. Usually, the test statistic that has the highest power of test is used.
T-test is the hypothesis test that uses the t-statistic. As already discussed earlier, T-statistic is used when the population variance is unknown, the sample size is large, or the sample size is small but the distribution of the population is normal or approximately normal.
Z-test is the hypothesis test that uses a z-statistic. Z-test is used when the population is normally distributed. When the population variance is known the z-statistic is given as,