Discussion
If population size N is very large, then the approximate value of minimum sample size for estimating population mean with desired accuracy under SRSWOR design is :
where \(\alpha\) and d are \(P[|\overline{Y} - \overline{y}| \lt d] \ge 1 - \alpha\)
Answer: D
The minimum sample size is approximately \(\left(\frac{s_{y} Z_{\alpha/2}}{d}\right)^{2}\).
Under SRSWOR, \(\mathrm{Var}(\overline{y}) = \left(\frac{1}{n} - \frac{1}{N}\right)s_{y}^{2}\). The accuracy condition \(P[|\overline{Y} - \overline{y}| \lt d] \ge 1 - \alpha\) requires \(Z_{\alpha/2}\sqrt{\mathrm{Var}(\overline{y})} \le d\):
\[ \begin{aligned} \frac{1}{n} - \frac{1}{N} &= \frac{d^{2}}{Z_{\alpha/2}^{2} s_{y}^{2}} \\ n_{0} &= \left(\frac{s_{y} Z_{\alpha/2}}{d}\right)^{2} \text{ when N is large} \end{aligned} \]
For finite N the correction is \(n = \frac{n_{0}}{1 + n_{0}/N}\).
The square root (option A) and dividing by d rather than \(d^{2}\) (option C) get the dimensions wrong, and \(\sqrt{N}\) has nothing to do with the accuracy required.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development