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 $Z_{0.025}=1.96$)

49

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: $49$