Question

In 1983, a random sample of 1000 scientists included 212 female scientists. A similar random sample of scientists in 1990 included 272 women. Do these figures indicate an increase in the population proportion of scientists who are women?

Answer 1

Yes, because 95% one-tailed confidence interval is (0, r),
where r=212/1000+Z_0.95 * SQRT (212*(1000-212)/1000³)=0.233,
and the new proportion is more than right bound :
272/1000=0.272 > 0.233
And we reject hypothesis about that proportion is equal or less than 0.212.