Trying to finish an assignment: What happens to the power of the z test when the standard deviation increases? and Is the shape of a sampling distribution always the same as that of the null hypothesis population? Thanks!
As the SD increases, the exactness of the estimate of a population mean is less.
The null hypothesis usually assumes a normal distribution. As I mentioned in your later post, assu7ming that the distribution isdue to chance factors, the sampling distribution will approximate a normal distribution more closely as the sample size increases.
I hope this helps a little more. Thanks for asking.