Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 18 - Introduction to Statistical Inference (2b of 3 discussion 1)

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2026-01-17T21:14:49-08:00

Here's our answer:
We are 95% confident that 7.4% to 13.4% of all US. births are preterm this year.

Here's our work:

Check the conditions for normality:

If 12% of births are preterm in 500 births, then here are the expected number of successes (preterm births) and the expected number of failures (full-term births).

Expected number of successes (preterm births):

Expected number of successes (full-term births):

So the conditions are met and we can use a normal model for the sampling distribution. This means we can say that about 95% of the results from random samples will estimate the true percentage of U.S. preterm births within 2 standard errors.

Calculate the standard error:

Calculate the 95% confidence interval:

sample proportion ± 2(standard error)

(52 / 500) 2(0.015)

0.104 0.03

0.074 to 0.134 (7.4% to 13.4%)