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.

Expert's answer

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.

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.

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