Confidence Intervals

This article proposes two improved family of estimators for estimating the finite population mean in simple random sampling (SRS) and stratified random sampling (S t RS). The proposed estimators always perform better than a family of ratio estimators suggested by Khoshnevisan et al. (2007) in SRS and Koyuncu and Kadilar (2009a) in S t RS. They also perform better than the ratio estimator given by Gupta and Shabbir (2008) in SRS and Koyuncu and Kadilar (2010) and Shabbir and Gupta (2011) in S t RS. The expressions for bias and mean squared error (MSE) of considered estimators are obtained. The results are illustrated by real data sets.

Even though chemistry is the foundation and gatekeeper of other science courses, high school students across continue to score poorly in the subject overall. The purpose of the study was to determine how the performance of learners in chemistry was related to the availability of chemistry lab materials. Kilifi North Constituency was the site of the study. Six mixed schools were chosen using simple random sampling, one school for girls and boys were chosen using purposive method. Eighty students were chosen using simple random selection and stratified random sampling. Eight chemistry teachers were sampled using basic random sampling and purposeful sampling. The Chemistry Teacher Questionnaire (CTQ), Student Questionnaire (SQ), Observation Checklist (OC), and document and mark sheet analysis were used to gather data. Ten students and two teachers participated in the pilot project which was conducted at two schools in the Kilifi North Constituency. Data analysis was made simplified with the use of the Statistical Package for Social Sciences (SPSS). The study variables were presented using descriptive statistics such as frequency tables, mean, and percentages. Hypotheses at .05. were tested using inferential statistics (Spearman's Rank order correlation and Pearson product moment of correlation coefficient). The study revealed that 75% of schools had laboratories, with a significant correlation (r = 0.819, p = 0.013) between the availability of laboratory materials and students' academic performance in chemistry practical’s, accounting for 67.08% of the variability in scores. Additionally, the majority of chemistry apparatus and chemicals were deemed sufficiently available, indicating overall adequacy in laboratory resources for effective teaching and learning. The study recommended that Schools should improve laboratory facilities by assuring the availability of necessary equipment and chemicals, as well as offering teacher training, in order to maximize resource efficiency and increase student chemistry performance.

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are studied under second order approximation. In third paper some estimators are proposed in two-phase sampling and their properties are studied in the presence of non-response. In fourth chapter a family of median based estimator is proposed in simple random sampling. In fifth paper some difference type estimators are suggested in simple random sampling and stratified random sampling and their properties are studied in presence of measurement error.

Background The study aimed at determining the effect of monitoring and evaluation planning on the performance of USE schools in Kinyamaseke Town Council, Kasese District Methodology A descriptive survey with both qualitative and quantitative methods were employed among all staff responsible for the implementation of the M&E in Kinyamaseke Town Council. Both simple random and purposive sampling were used to select the 79 staff. Simple random sampling was used to give an equal chance of teachers to be selected. Purposive sampling was used to select MoES official, DEO DSI, headteachers and their deputies. The key informants were selected purposively on the basis of having knowledge on the subject matter under investigation. The researcher administered questionnaires and interview guides to get the information. Results Study findings revealed that there is, “a very strong linear relationship (Multiple R = .807) between the combined of dimensions of M&E planning (M&E goal setting and M&E budgeting) and performance of USE schools”. Conclusion Findings of this study revealed that M&E planning plays an important role in the performance of USE schools. For M&E planning to be taken seriously, senior management must show that they believe it can play an important strategic role. Recommendation There is need for the Ministry of Education and Sports to improve M&E planning in order to improve performance of USE schools. This can be achieved by first taking into consideration of setting clear polies to budget and allocate resources for M&E and then M&E goal setting.

This paper deals with estimation of population median in simple and stratified random samplings by using auxiliary information. Auxiliary information is rarely used in estimating population median, although there have been many studies to estimate population mean using auxiliary information. In this study, we suggest some estimators using auxiliary information such as mode and range of an auxiliary variable and correlation coefficient. We also expand these estimators to stratified random sampling for combined and separate estimators. We obtain mean square error equations for all proposed estimators and find theoretical conditions. These conditions are also supported by using numerical examples.

The main purpose of this study was to examine Social Studies teachers’ competence in teaching and assessing learning outcomes in affective domain in senior high schools in the Aowin Municipality in Western North Region in Ghana. A quantitative approach was used in this study as it allowed the researchers to carry out an objective analysis and generate factual knowledge through measurement. The survey design was used for the study. The study population constituted Social Studies teachers in the 40 Junior High Schools in the Aowin Municipality of the Western North Region of Ghana. Simple random and convenient sampling techniques were used to select the schools and respondents for the study. The simple random sampling was used to select 20 schools to participate in the study. This was to provide an equal opportunity for each school to participate in the study. From these selected schools, a convenience sampling technique was used in selecting forty (40) teachers (two from each school in the Aowin Municipality where Social Studies is offered as a core subject. The main instrument used for the study was structured questionnaire. Descriptive statistics in the form of percentages was used to analysis the data in this study. The study concluded that Social Studies teachers hardly teach and assess directly in the affective outcome, hence the affective domain is neglected in the teaching and learning of the subject. It is recommended that the universities and other training institutions should strengthen the teaching on the use of the techniques for assessing the affective domain. In-service training courses should also be organised regularly for social studies teachers on the use of the techniques for the assessment of affective domain.

Ranked Set Sampling and Ranked Set Sampling concomitant are more efficient than Simple Random Sampling. This can be determined by calculating the Relative Precision which is a ratio value from the variance of the mean from each sampling technique. From the research of Ranked Set Sampling, obtained , and so Ranked Set Sampling is more efficient than Simple Random Sampling. For the research of Ranked Set Sampling concomitant, obtained , and so Ranked Set Sampling concomitant is more efficient than Simple Random Sampling, and for simple linear regression analysis obtained , , , so simple linear regression model of Ranked Set Sampling is more efficient than simple linear regression model of Simple Random Sampling

Two Stage Sampling procedure has been found to be much more acceptable for demographic surveys owing to the lower cost involved and also due to the fact that it gives rise to a good representative sample. .As such, it has been found to be much acceptable for estimating total fertility rate (TFR), an important measure of fertility. The objective of this paper is to estimate the TFR in the slum pockets of Guwahati city in Assam under two stage sampling technique and to bring out a comparative analysis of the TFR calculated under the proposed sampling design and under the Simple Random Sampling (SRS) method.The study reveals that the overall fertility scenario in the slum areas of Guwahati, as far as TFR is concerned, when calculated under two stage sampling technique is above the replacement level. However, the TFR calculated by SRS method is found to be almost equal to the replacement level, implying under estimation of TFR when calculated by this method. Moreover, it has been seen that the adjusted TFRs derived after adjusting the biases marginally increases in case of SRS technique and decreases in case of two stage sampling technique. The MSE s are found to be higher in case of conventional technique, implying that the sampling error involved in the conventional method is more as compared to two stage sampling technique. We may thus consider two stage sampling method as a better technique for estimating TFR.

Chapter 8 - Random Sampling: Planning Ahead for Data Gathering

In this pandemic where teachers are so worried about their health and some other factors that affect their well-being including mental health. This research have examined and explored the effectiveness of hands-on school-based gardening as intervention on the teachers’ well-being amidst pandemic. A mixed-method research design with cluster sampling technique – simple random sampling was utilized in the study with a 50% response rate. Results showed that teacher-participants strongly agree that everyone can benefit from gardening like social benefits, nutritional benefits, and physical activity improves one’s physical, social, and mental health. Teachers displayed very good disposition towards gardening. In the level of happiness, teachers have shown significant improvement after being exposed and engaged to hands-on school-based gardening and believed that gardening activities have positive influences on health and well-being of the person. Recurring themes among teacher-participants indicate importance to engage oneself in the gardening activities to increase social interaction, communication, motivation, task engagement, relieving stress, and improve people’s health and well-being. It is of interest to embrace gardening at home. Further studies may be conducted integrating gardening in the lessons among students to understand how effective gardening in their academic performance and point ways on facing life’s challenges.

In this article, we propose an exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling. The properties of the proposed estimator are obtained and comparison is made with some of the existing estimators. The proposed estimator is found to perform better than the usual mean, ratio, exponential ratio, traditional regression and Pandy (1980) estimators in simple and stratified random sampling. We use six data sets for simple random sampling case and two data sets for stratified random sampling case to compare the performances of all of the estimators considered here.

Research on several forms of ranked set samples had been done by many researchers recently for estimating the population mean and other parameters. The results have ascertained that the ranked set samples are proven to be more efficient than the simple random samples in many situations. In this paper, modified bivariate ranked set sample (MBVRSS) was introduced to estimate a simple linear regression model when the regressors were assumed to be random. A primary data was collected on age and height in meter of 200 people from Ijebu-North Local Government Area of Ogun State. It is then shown that MBVRSS gives unbiased and highly efficient estimators of the regression model parameters, than those obtained by using bivariate simple random sampling (BVSRS), RSS or BVRSS using the same number of sample size. Key words: Modified bivariate ranked set sampling (MBVRSS), bivariate ranked-set sampling (BVRSS), bivariate simple random sampling (BVSRS) ranked set sampling (RSS), simple random sampling (SRS), simple linear regression.

ABSTRACTIn this paper, single-phase mixture regression cum ratio estimators are presented by utilizing auxiliary variables and auxiliary attributes simultaneously under stratified random sampling. Special cases of these estimators are discussed and further mean square errors are extracted mathematically. Also, to observe the properties of proposed estimators, simulation technique is used which shows that the distribution of the proposed estimators is approximately normal. To differentiate the performance of the proposed estimators, an empirical study has been conducted by incorporating quantitative and qualitative characteristics in the form of auxiliary attributes and variables simultaneously. Comparisons are made with single-phase mixture regression cum ratio estimators under simple random sampling. It has been found that the mixture regression cum ratio estimators employing multiple auxiliary variables and attributes, simultaneously, under stratified random sampling are more efficient than mixture regression cum ratio estimator under simple random sampling.

This study investigated the influence of Teachers’ instructional strategies and students’ learning styles on academic achievement in physics among Kenyan high school students. A quasi–experimental pre-test post–test non-equivalent control group design was employed to investigate how three teachers' instructional strategies (guided-inquiry, cooperative learning and direct instruction) and three learning styles (visual, auditory and kinaesthetic) influence academic achievement in Physics practical work while controlling for gender. The target population was all form three Physics students in Navakholo Sub-County area of Kakamega County. A sample size of five hundred and nineteen (519) form three physics students were selected through multistage sampling procedures (purposive sampling, proportionate stratified random sampling and simple random sampling). One null hypothesis was tested at 0.05 level of significance to guide the study. Physics Achievement Tests 1 and 2 (PAT 1 & PAT 2 ) and Learning Style Questionnaire. Teachers’ Instructional Guides on Guided-Inquiry (TIGITS), Cooperative (TIGCTS) and Direct Instructional Strategy (TIGDITS) were used to collect data. Validity and reliability of the instruments were assessed. Analysis of covariance (ANCOVA), Multiple Classification Analysis (MCA) and Scheffe multiple comparison test were used to analyse the data. Findings revealed, a significant effect on the academic achievement of physics students taught with different instructional strategies considering their different learning styles. Recommendations were provided. Article visualizations:

This paper considers whether random sampling always produces more accurate survey results in the case of South Korea. We compare information from the 2010 census to the demographic variables of three public opinion surveys from South Korea: Gallup Korea's Omnibus Survey (Survey A) is conducted every two months by Gallup Korea; the annual Social Survey (Survey B) is conducted by Statistics Korea (KOSTAT); the Korean General Social Survey (KGSS or Survey C) is conducted annually by the Survey Research Center (SRC) at Sungkyunkwan University (SKKU). Survey A uses quota sampling after randomly selecting the neighborhood and initial addresses; Survey B uses random sampling, but allows replacements in some situations; Survey C uses simple random sampling. Data from more than one year was used for each survey. Our analysis suggests that Survey B is the most representative in most respects, and, in some respects, Survey A may be more representative than Survey C. Data from Survey C was the least stable in terms of representativeness by geographical area and age. Single-person households were underrepresented in both Surveys A and C, but the problem was more severe in Survey A. Four-person households and married persons were both over-represented in Survey A. Less educated people were under-represented in both Survey A and Survey C. There were differences in income level between Survey A and Survey C, but income data was not available for Survey B or the census, so it is difficult to ascertain which survey was more representative in this case.