ABSTRACT
A problem of the ratio-type estimators in Stratified Sampling is the use of non-attribute auxiliary information. In this study, some ratio-type estimators in stratified random sampling using attribute as auxiliary information are proposed. The sample mean of study variable and proportion of auxiliary attribute were transformed linearly and using auxiliary parameters respectively. Biases and mean square errors (MSE) for these estimators were derived. The MSE of these estimators were compared with the MSE of the traditional combined ratio estimator. The results show that the proposed estimators are more efficient and less bias than the combined ratio estimate in all conditions. An empirical study was also conducted using students height data from each faculty of the Usmanu Danfodiyo University, Sokoto. The results also show that the proposed estimators are more efficient and less bias than the combined ratio estimator. In addition, formulae for determination of sample sizes when the proposed estimators are adopted under various allocations (Optimum, Neyman and Proportional) for fixed cost and desired precision were obtained.
TABLE OF CONTENTS
TITLE PAGE
TABLE OF CONTENTS
LIST OF TABLES
ABBREVIATIONS/NOTATIONS
ABSTRACT
CHAPTER ONE: INTRODUCTION
1.1 INTRODUCTION
1.2 CENSUS VERSUS SAMPLE SURVEY
1.3 RANDOM SAMPLING
1.4 DEFINITION OF BASIC TERMS
1.5 AIM AND OBJECTIVES
1.6 SIGNIFICANCE OF THE STUDY
1.7 SCOPE AND LIMITATION
CHAPTER TWO: LITERATURE REVIEW
2.1 RATIO ESTIMATORS
2.2 RANKED SET SAMPLING
2.3 STRATIFIED RATIO ESTIMATOR
CHAPTER THREE: MATERIALS AND METHODS
3.1 INTRODUCTION
3.2 DATA USED FOR THE ANALYSIS
3.3 SOFTWARE USED FOR THE ANALYSIS
3.4 PROPOSED ESTIMATORS
3.5 BIAS AND MEAN SQUARE ERROR (MSE) OF ESTIMATOR T
3.6 BIAS AND MEAN SQUARE ERROR OF THE PROPOSED ESTIMATORST
3.7 EFFICIENCY COMPARISONS
3.8 PROPERTIES OF THE PROPOSED ESTIMATORS
3.9 DETERMINATION OF SAMPLE SIZE
3.9.1 Constants of Proportionality for Fixed Cost
3.9.2 Constants of Proportionality for Fixed precision
CHAPTER FOUR: EMPIRICAL STUDY
4.1 PRE-AMBLE
4.2 RESULTS AND DISCUSSION
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 SUMMARY
5.2 CONCLUSION
5.3 RECOMMENDATION
REFERENCES
APPENDIX
CHAPTER ONE
INTRODUCTION
1.1 INTRODUCTION
Prior knowledge about population mean along with coefficient of variation, kurtosis and correlation of the population of an auxiliary variable are known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a variable of interest. The use of auxiliary information can increase the precision of an estimator when study variable is highly correlated with auxiliary variable. Srivastava and Jhajj (1981) suggested a class of estimators of the population mean, provided that the mean and variance of the auxiliary variable are known. Singh and Tailor (2003) considered a modified ratio estimator by exploiting the known value of correlation coefficient of the auxiliary variable. Singh and Upadhyaya (1999) suggested two ratio-type estimators when the coefficient of variation and kurtosis of the auxiliary variable are known.
However, the fact that the known population proportion of an attribute also provides similar type of information has not drawn as much attention. In several situations, instead of existence of auxiliary variables there exists some auxiliary attributes, which are highly correlated with study variable (Singh et. al.,2008). For example, sex and height of the persons, amount of milk produced by a particular breed of cow, amount of yield of wheat crop by a particular variety of wheat etc. (Jhajj et. al., 2006). In such situations, taking the advantage of point-biserial correlation between the study variable and the auxiliary attribute, the estimators of parameters of interest can be constructed by using prior knowledge of the parameters of auxiliary attribute....
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