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?

Hint: Construct the 95% CI for the difference in proportions and examine whther
that CI contains zero.

Answer 1

Answer is yes, because 95% one-tailed confidence interval is (0, r),

where r = 212/1000 + Z_0.95 * √(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.