Question

Income Inequality ~ A random sample of 110 students at a top-ten university were asked if they believe that the federal government should make reducing income inequality a top priority. The estimated standard error of the sample proportion was found to be 0.0477.

A normal distribution can be used to model the sampling distribution of sample proportion. The researchers constructed a confidence interval for the actual proportion of students who believe that the federal government should make reducing income inequality a top priority.

Following that, they collect a new sample of 200 students and find that the sample proportion is the same as the first sample proportion.

Consider the statement:

The estimated standard error for the sample proportion based on the new sample is less than the first sample's standard error.

Is this statement always true or sometimes true or never true?

Question 13 options:

	Always true
	Sometimes true
	Never true

Answer 1

since standard error of sample =√p^*(1-p^)/n)

therefore standard error of sample decreases as sample size increases given p^ remains fixecd

therefore it is always true