Think about the z statistic for a one sample test about the

Think about the z statistic for a one sample test about the population mean. The mathematical formula for this test statistic has standard error in the denominator. The formula for standard error in turn has square root of sample size, n in the denominator. Thus, the z statistic for a one sample test about the population mean is directly proportional to the square root of sample size. Hence, there is always some sample size n at which the observed z value will exceed the corresponding critical z value. In other words, if the researcher (or analyst) has the freedom to increase sample size, then she can reject the null hypothesis at will. The statistical significance in such a case thus becomes meaningless.

Please comment on this issue (i.e. statistical significance not being much informative). What can we do in order to counter this issue with null hypothesis significance testing?

Solution