If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation $σ = 50$, then the size of the sample in the study is: (Given $Z_{0.025}=1.96$)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 49
95% CI: $132$ to $160$
Margin of error:
$E=\frac{160-132}{2}=14$
Formula:
$E = Z_{0.025}\,\frac{\sigma}{\sqrt{n}}$
$14 = 1.96 \cdot \frac{50}{\sqrt{n}}$
$14 = \frac{98}{\sqrt{n}}$
$\sqrt{n} = \frac{98}{14} = 7$
$n = 49$
Final answer: $49$