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 $Z_{0.025}=1.96$)
Answer & explanation
Correct answer: option 4
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 $n=54$.