A 95% confidence interval for a population mean was reported to be 152 to 160, if sample standard deviation $σ=15$, then sample size used in this study is (Given $Z_{0.025}=1.96$)

54

The correct answer is Option (4) → 54

$\text{Confidence interval }=(152,160)$

$\text{Sample mean } \bar{x}=\frac{152+160}{2}=156$

$\text{Margin of error }=160-156=4$

$\text{For }95\%\text{ CI}$

$\bar{x}\pm Z_{0.025}\frac{\sigma}{\sqrt{n}}$

$4=1.96\frac{15}{\sqrt{n}}$

$\sqrt{n}=\frac{1.96\times15}{4}$

$\sqrt{n}=7.35$

$n=(7.35)^2\approx54$

The sample size used is $n=54$.