Cpt sampling theory revision sheet
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This document provides a revision sheet on sampling theory. It outlines three types of problems: 1) Problems based on standard error, which involve calculating the standard error of the sample mean or proportion from a finite or infinite population. 2) Problems based on confidence intervals, which involve determining confidence limits or intervals for population means or proportions based on the sample data. 3) Problems based on estimation, which involve calculating values of z for a given sample mean or determining required sample sizes to estimate a mean within a given level of error or confidence level. It provides examples of confidence levels and intervals. Finally, it lists revision problems from ICAI on sampling theory.
Cpt sampling theory revision sheet
- 1. Sampling Theory Revision Sheet December 2, 2010 Sampling-Theory of Estimation Types of Problems 1) Type-1: Problem based on Standard Error (S.E.) a) In case the Population is either infinite or in which samples are drawn from a finite population with replacement. i. S.E. for sample mean( ̅ ) ̅ √ √∑( ̅) √ Where ̅ sample size ii. S.E. for sample proportion √ √ Where p population proportion sample size. b) In case the Population is finite (generally whenever the ratio of sample size (n) to population size (N) is 0.05 or more) In other words when sampling fraction (n/N) is 0.05 more. i. S.E. for sample mean ( ̅) ̅ √ √ √∑( ̅) √ √ Where ̅ population size sample size VXplain 2 Score More – post your doubts to us at vxplain@gmail.com Page 1
- 2. Sampling Theory Revision Sheet December 2, 2010 ii. S.E. for sample proportion √ √ √ √ Where p population proportion population size sample size. 2) Type-2: Problem based on Confidence Interval i) Determination of Confidence Limits or Limits of Parameters for Population Mean ( ̅ ): Confidence Limits Confidence Interval Confidence Level Minimum Maximum ̅ ̅ ̅ 68.27% ̅ ̅ ̅ 90% ̅ ̅ ̅ 95% ̅ ̅ ̅ 95.45% ̅ ̅ ̅ 98% ̅ ̅ ̅ 99% ̅ ̅ ̅ 99.73% ii) Determination of Confidence Limits or Limits of Parameters for Population Proportion (p): Replace ̅ by p in above table. Where p is sample proportion. 3) Type-3: Problem based on Estimation. ̅ i) Value of Z for given Sample Mean is ̅ ii) Sample Size ( ̅) for estimating a mean is ̅ ( ) ( ) iii) Sample Size ( ) for estimating a mean is ( ) Where,E is an error Z corresponding to percentage Confidence Level (e.g. for 95% Confidence Level Z VXplain 2 Score More – post your doubts to us at vxplain@gmail.com Page 2
- 3. Sampling Theory Revision Sheet December 2, 2010 Revision Problems from ICAI 1) Page no. 15.25 Set A: Theory based question. 2) Page no. 15.28 Set B: a. Type 1 based Questions (Q1 to Q8), b. Type 1& Type 2 based Questions (Q8 to Q15). VXplain 2 Score More – post your doubts to us at vxplain@gmail.com Page 3