True or False: The standard error of the sample proportion and the standard deviation of the sample proportion are usually the same.

False

Step-by-step explanation:

They are not the same. If your sample is small, you might see a big difference between both numbers. Only when the sample is big enough the numbers are similar.

If each element of the sample has Normal Distribution, if you take the mean distribution and substract from it the mean, dividing by the standard error will give you a T-Student Distribution with as much degrees of freedom as the sample length. On the other hand, if you divide it instead by the standard deviation of the sample, you will obtain a Normal Distribution.