If 95% confidence interval for the population mean was reported to be 140 to 150 and $σ = 25$, then size of the sample used in this study is:
[Given: $Z_{0.025}=1.96$]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 96
Given:
Confidence interval: 140 to 150
Population standard deviation: σ = 25
95% confidence interval → Z₀.₀₂₅ = 1.96
Confidence interval formula:
$\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$
Margin of error (E) = (150 - 140)/2 = 5
$E = Z \frac{\sigma}{\sqrt{n}}$
$5 = 1.96 \frac{25}{\sqrt{n}}$
$\sqrt{n} = \frac{1.96 × 25}{5}$
$\sqrt{n} = \frac{49}{5} = 9.8$
$n = (9.8)^2 \approx 96.04$
Sample size n ≈ 96