GATE 2026 AR — Planning – Question 47
A sample of 1250 must reproduce the city age/sex proportions. Percentages(Male, Female) by age are 0–6:(2, 1.5), 7–18:(8.5, 6), 19–25:(14.5, 13.5), 26–40:(14.5, 11), 41–50:(12, 8), 51–60:(2.5, 2.5), 60+:(1.5, 2). Find required female respondents aged 19–40, to the nearest integer.
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Correct answer: 305 to 307
Explanation
The desired two female age categories constitute 13.5%+11%=24.5% of the entire population. Required sample count is 1250×0.245=306.25, rounding to 306. Do not renormalise within females because the supplied percentages already refer to the total city population.