Question

Consider taking a random sample from a population with p = 0.25. What is the standard error of p-hat for random samples of size 400? Round to four decimal places. Would the standard error of p-hat be smaller for random samples of size 200 or samples of size 400? 400 Does cutting the sample size in half from 400 to 200 double the standard error? yes/no

Answer 1

Answer:

a)

To determine the standard error of sample proportion

p^ = 0.25

n = 400

consider,

standard error = sqrt(p^(1 - p^)/n)

substitute values

standard error = sqrt(0.25(1 - 0.25)/400)

= sqrt(0.25*0.75/400)

= 0.02165

standard error = 0.0217

b)

Here due to the larger size of sample size i.e., 400 the standard error of proportion is smaller.

c)

Now standard error = sqrt(p^(1 - p^)/n)

= sqrt(0.25(1 - 0.25)/200)

standard error = 0.0306

here by cutting the 400 to 200 i.e., sample size it raises the standard error to 1.41