If 95% confidence interval for the population mean was reported to be 140 to 150 and \(\sigma = 25\), then size of the sample used in this study is:
[Given: \(Z_{0.025} = 1.96\)]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 96
A 95% confidence interval for the mean is \(\bar{x} \pm 1.96\frac{\sigma}{\sqrt{n}}\). Its half-width is the margin of error:
\( \displaystyle E = \frac{150 - 140}{2} = 5 \)
\( \displaystyle 5 = 1.96 \times \frac{25}{\sqrt{n}} \)
\( \displaystyle \sqrt{n} = \frac{1.96 \times 25}{5} = 9.8 \)
\(n = (9.8)^2 = 96.04\)
So the sample size is about 96.