A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $σ = 15$, Then the sample size is: ($Z_{.025}=1.96$)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 54 **
95% confidence interval: $152$ to $160$
Mean $=156$ and margin of error:
$E = 160 - 156 = 4$
Formula for confidence interval margin:
$E = Z_{\alpha/2}\,\frac{\sigma}{\sqrt{n}}$
Substitute values:
$4 = 1.96\,\frac{15}{\sqrt{n}}$
Solve for $n$:
$\sqrt{n} = 1.96 \cdot \frac{15}{4}$
$\sqrt{n} = 1.96 \cdot 3.75 = 7.35$
$n = 7.35^{2} \approx 54.02$
Sample size ≈ 54