Recall the formula for a proportion confidence interval is

p^zp^(1p^)n

Thus, the margin of error isE=zp^(1p^)nE=zp^(1p^)n.

NOTE: themargin of errorcan be recovered after constructing a confidence interval on the calculator using algebra (that is, subtracting p^p^ from the right endpoint.)

In a simple random sample of size 59, taken from a population, 22 of the individuals met a specified criteria.

a) What is the margin of error for a 90% confidence interval for p, the population proportion?

Round your response to at least 4 decimal places.

b) What is the margin of error for a 95% confidence interval for p?

Round your response to at least 4 decimal places.

NOTE: These margin of errors are greater than .10 or 10%.

c) How big of a sample is needed tobe certainthat we have a margin of error less than .10 (or 10%) at 90% confidence?

d)How big of a sample is needed tobe certainthat we have a margin of error less than .10 (or 10%) at 95% confidence?