If 95% confidence interval for the population mean was reported to be 160 to 170 and \(\sigma = 25\), then size of the sample used in this study is:
(Given \(Z_{0.025} = 1.96\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 96
The 95% confidence interval for the mean is
\( \displaystyle \bar{x} \pm Z_{0.025}\,\frac{\sigma}{\sqrt{n}} \)
Its half-width (the margin of error) is half the length of the interval:
\( \displaystyle E = \frac{170 - 160}{2} = 5 \)
\( \displaystyle 1.96 \times \frac{25}{\sqrt{n}} = 5 \)
\( \displaystyle \sqrt{n} = \frac{1.96 \times 25}{5} = 9.8 \)
\(n = 9.8^2 = 96.04 \approx 96\)