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 $Z_{0.025}=1.96$)
Answer & explanation
Correct answer: option 3
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,
$E=Z_{α/2}×\frac{σ}{\sqrt{n}}$
$5=1.96×\frac{15}{\sqrt{n}}$
$⇒\sqrt{n}=\frac{1.96×15}{5}$
$⇒n≃35$