# Answer to Question #2406 in Statistics and Probability for Damien

Question #2406

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.

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.

Expert's answer

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

where r = 212/1000 + Z

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.

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.

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