GATE 2022 PI – Question 38
A normally distributed parameter was surveyed with n = 1000, giving confidence interval [500,700], mean 600. What sample size gives [550,650] at the same confidence level?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (B) 4000
Explanation
With unchanged population variability and confidence, interval half-width is proportional to $1/\sqrt n$. Halving width from 100 to 50 requires four times the sample: $n_2=1000(100/50)^2=\mathbf{4000}$, **B**.