Question

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

Answer 1

The standard error of the sample proportion and the standard deviation of the sample proportion are usually the same.

(True)

Step-by-step explanation:

While the standard error of the sample proportion and the standard deviation of the sample proportion are indeed calculated using the same formula, it's essential to understand the nuanced differences between them. The standard error is a measure of how much the sample proportion is expected to vary from the true population proportion due to sampling variability. It provides an estimate of the uncertainty associated with using a sample to make inferences about a population.

On the other hand, the standard deviation of the sample proportion is a measure of the variability of sample proportions in different random samples. In essence, it gives us a sense of how much individual sample proportions are expected to deviate from the mean of all possible sample proportions.

Answer 2

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.