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The classical normal curve approximation to cumulative hypergeometric probabilities requires that the standard deviation of the hypergeometric distribution be larger than three which limits the usefulness of the approximation for small populations. The purposes of this study are to develop clearly-defined rules which specify when the normal curve approximation to the cumulative hypergeometric probability distribution may be successfully utilized and to determine where maximum absolute differences between the cumulative hypergeometric and normal curve approximation of 0.01 and 0.05 occur in relation to the proportion of the population sampled.

Dynamic interactive technology brings new opportunities for helping students learn central statistical concepts. Research and classroom experience can be help identify concepts with which students struggle, and an \"action-consequence\" pre-made technology document can engage students in exploring these concepts. With the right questions, students can begin to make connections among their background in mathematics, foundational ideas that undergrid statistics and the relationship these ideas. The ultimate goal is to have students think deeply about simple and basic statistical ideas so they can see how they lead to reasoning and sense making about data and about making decisions about characteristics of a population from a sample.Technology has a critical role in teaching and learning statistics, enabling students to use real data in investigations, to model complex situations based on data, to visualize relationships using different representations, to move beyond calculations to interpreting statistical processes such as confidence intervals and correlation, and to generate simulations to investigate a variety of problems including laying a foundation for inference. Thus, graphing calculators, spreadsheets, and interactive dynamic software can all be thought of as tools for statistical sense making in the service of developing understanding.

Orientador: Prof. Dr. André Ricardo Oliveira da Fonseca / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016. / No mundo contemporâneo é comum constantes pesquisas em diversos âmbitos, tanto sociais, quanto econômicos, entre outros. Para tais pesquisas é fundamental a coleta de dados, organizar os dados, como também construir tabelas e gráficos estatísticos, entretanto é inadmissível não haver uma interpretação consistente sobre os resultados. Desta forma, o objetivo deste trabalho é introduzir os alunos do Ensino Médio, especificamente os do terceiro ano, na teoria da inferência estatística, por meio de atividades experimentais, para que eles possam, num nível elementar, desenvolver as primeiras compreensões a respeito dos meios de obtenção de uma amostra e das conclusões possíveis sobre a respectiva população. Assim, estimulando os educandos em buscar constantemente informações sobre pesquisas estatísticas, as quais estarão presentes em vários momentos da sua vida em sociedade. / In the contemporary world it is common to come across frequent research from various scopes, both social and economical amongst others. For such research, it is vital to collect data, organize it as well as put together statistical charts and graphs. However it is unacceptable that there is no consistent interpretation about the results. Therefore, the objective of this work is to introduce High School students, more specifically the seniors, to the theory of statistical inference, through experimental activities, so that they can, at an elementary level, develop their primary understanding of both the means to obtain a sample and the possible conclusions drawn about its respective population. Thus, we expect to stimulate the students to constantly seek information about statistical research, which will be present in many different moments in their lives as part of society.

Orientador: Jose Guilherme Cecatti / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Ciencias Medicas / Made available in DSpace on 2018-08-08T20:46:57Z (GMT). No. of bitstreams: 1 Barbieri_Cristiane_M.pdf: 3185188 bytes, checksum: b566f66bd024181e78245a8dd5211fe7 (MD5) Previous issue date: 2007 / Resumo: Introdução: mais recentemente, demonstrou-se que o diâmetro do cordão umbilical pode se modificar nos casos de diabetes mellitus, pré-eclâmpsia, restrição de crescimento intra-uterino e baixo peso ao nascimento, podendo talvez ser utilizado como um marcador para detecção precoce destas condições. Objetivo: obter intervalos de referência das medidas ultra-sonográficas da área do cordão umbilical, dos diâmetros de seus vasos e da área da superfície da Geléia de Wharton da secção transversa do cordão umbilical em função da idade gestacional em gestações de baixo risco, entre 12 e 40 semanas, avaliar a variabilidade inter- e intra-observador destas medidas e investigar sua correlação com o peso fetal estimado. Método: foram avaliadas 2310 gestantes no período entre junho de 2005 e dezembro de 2006, seguindo critérios de inclusão e exclusão pré-estabelecidos. Em uma sub-amostra destas gestantes foi avaliada a variabilidade inter- e intraobservador, estimando-se o coeficiente de correlação de Spearman, o coeficiente de correlação intra-classe e o alfa de Crombach. Para cada idade gestacional, foi avaliado um número mínimo de 59 casos, calculando-se a média e seu respectivo desvio-padrão e os percentis 10, 50 e 90 de cada uma das medidas. Para a análise estatística foram utilizados os testes t de Student, Anova e Wilcoxon para amostras independentes. Os intervalos de referência foram estimados por regressão polinomial de terceiro grau. Foi avaliado também o desempenho da área da secção transversa do cordão umbilical, do diâmetro do cordão umbilical e da área de geléia de Wharton do cordão umbilical em predizer alterações do peso fetal estimado (PFE) nestas gestações, estimando-se sua sensibilidade, especificidade, valor preditivo positivo e negativo. Resultados: Foram obtidas elevadas correlação, reprodutibilidade e confiabilidade na avaliação da variabilidade inter e intra-observador das medidas do cordão umbilical e de seus vasos. Os intervalos de referência apresentaram valores crescentes até cerca de 32 semanas e depois estabilizaram-se. As medidas avaliadas apresentaram baixa sensibilidade para predição de alterações do PFE. Portanto, elas não devem ser utilizadas para rastreamento com esta finalidade. Conclusões: os valores normais padronizados para essas medidas em todas as idades gestacionais, para gestações de baixo risco na população de referência, foram determinados, havendo a necessidade de que sejam posteriormente validados como preditores de situações perinatais adversas / Abstract: Introduction: recently it has been demonstrated that the diameter of the umbilical cord may be modifyed in the case of diabetes, preeclampsia, intrauterine growth restriction and low birthweight. In this way it could perhaps be used as a marker for early detection of these conditions. Objective: to obtain reference ranges for the ultrasonographic measurements of the umbilical cord area, the diameters of its vessels and the area of the Wharton Jelly surface from a cross sectional plan of the umbilical cord according to gestational age in low risk pregnancies between 12 and 40 weeks; to evaluate the inter- and intra-observer variability of these measurements; and to investigate their correlation with the estimated fetal weight. Method: a total of 2310 pregnant women were evaluated in the period from June 2005 and December 2006, following previously stablished inclusion and exclusion criteria. Inter and intra-observer variability were evaluated in a sub sample of these pregnant women, with the estimation of Spearman correlation coefficient, the intraclass correlation coefficient and alfa of Crombach. For each gestational age a minimum number of 59 cases were evaluated. For statistical analysis mean and standard deviation and the percentiles 10, 50 and 90 for each one of the measurements were estimated. Student t, Anova and Wilcoxon tests for independent samples were used. The reference ranges were estimated by third degree polynomial regression. The performance of the area of the transverse section of umbilical cord, its diameter and the area of the Wharton Jelly in predicting deviations of the estimated fetal weight (EFW) was also estimated among these pregnancies, with their sensitivity, specificity, positive and negative predictive values. Results: High correlation, reproductibility and feasibility were obtained when evaluating the inter- and intra-observer variability of the measurements of umbilical cord and its vessels. The reference intervals presented increasing values up to around 32 weeks, and afterwards they estabilized. The measurements evaluated showed very low sensitivity for predicting deviations of the EFW. Therefore they should not be used for screening with this purpose. Conclusions: the normal standardized values for these measurements in all gestational ages, for low risk pregnancies in the reference population, were determined. There is still the need of them being validated as predictors of adverse perinatal conditions / Mestrado / Tocoginecologia / Mestre em Tocoginecologia

Dynamic interactive technology brings new opportunities for helping students learn central statistical concepts. Research and classroom experience can be help identify concepts with which students struggle, and an \"action-consequence\" pre-made technology document can engage students in exploring these concepts. With the right questions, students can begin to make connections among their background in mathematics, foundational ideas that undergrid statistics and the relationship these ideas. The ultimate goal is to have students think deeply about simple and basic statistical ideas so they can see how they lead to reasoning and sense making about data and about making decisions about characteristics of a population from a sample.Technology has a critical role in teaching and learning statistics, enabling students to use real data in investigations, to model complex situations based on data, to visualize relationships using different representations, to move beyond calculations to interpreting statistical processes such as confidence intervals and correlation, and to generate simulations to investigate a variety of problems including laying a foundation for inference. Thus, graphing calculators, spreadsheets, and interactive dynamic software can all be thought of as tools for statistical sense making in the service of developing understanding.