A 95% confidence interval for a population mean was reported to be 160 to 170. If $σ=15$ then sample size used in this study is :

(Given $Z_{0.025}=1.96$)

35

The correct answer is Option (3) → 35

To determine the sample size (n),

Confidence Interval = $\bar x±Z_{α/2}×\frac{σ}{\sqrt{n}}$

Margin of  error, E = Upper limit - $\bar x$

$=\frac{170-160}{2}=5$

and,

$E=Z_{α/2}×\frac{σ}{\sqrt{n}}$

$5=1.96×\frac{15}{\sqrt{n}}$

$⇒\sqrt{n}=\frac{1.96×15}{5}$

$⇒n≃35$