what effect does increasing the sample size have on standard

what effect does increasing the sample size have on standard error and the test statisitc?

Solution

Effect of the increase in sample size on standard error :

The standard error (which represents the amount of sampling variability) is larger when the sample size is small and smaller when the sample size is large. So, when the sample size is small, it can be difficult to see a difference between the sample mean and the population mean, because there is too much sampling variability messing things up. If the sample size is large, it is easier to see a difference between the sample mean and population mean because the sampling variability is not obscuring the difference.

Effect of the increase in sample size on test statistic :

The primary goal of test statistics is to generalize from a sample to a population, it is less of an inference if the sample size is large. So , a large sample size is beneficial.