This chapter discusses sampling and sampling distributions. It aims to describe simple random sampling, explain the difference between descriptive and inferential statistics, define sampling distributions, and determine properties of key sampling distributions such as the mean, proportion, and variance. The key points are:
- Sampling distributions describe the distribution of all possible values of a statistic from samples of a given size from a population.
- The sampling distribution of the mean is normally distributed for large samples, with mean equal to the population mean and standard deviation equal to the population standard deviation over the square root of the sample size.
- Even if the population is not normal, the Central Limit Theorem states that the sampling distribution of the mean will be approximately normal for large
This chapter introduces basic probability concepts including sample spaces, events, simple probability, joint probability, and conditional probability. It defines key terms and provides examples of calculating probabilities using contingency tables and decision trees. Probability rules are examined, including the general addition rule and rules for mutually exclusive and collectively exhaustive events. The chapter also covers statistical independence, marginal probability, and Bayes' theorem for calculating conditional probabilities.
This chapter discusses various methods for organizing and presenting data through tables and graphs. It covers techniques for categorical data like summary tables, bar charts, pie charts and Pareto diagrams. For numerical data, it discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, frequency polygons and ogives. It also introduces methods for presenting multivariate categorical data using contingency tables and side-by-side bar charts. The goal is to choose the most effective way to summarize and communicate patterns in the data.
The Normal Distribution and Other Continuous DistributionsYesica Adicondro
The document describes concepts related to the normal distribution and other continuous probability distributions. It introduces the normal distribution and its properties including that it is bell-shaped and symmetric with the mean, median and mode being equal. It describes how the mean and standard deviation determine the location and spread of the distribution. It also covers translating problems to the standardized normal distribution and how to find probabilities using the normal distribution table and by calculating the area under the normal curve.
Some Important Discrete Probability DistributionsYesica Adicondro
The chapter discusses important discrete probability distributions used in statistics for managers. It covers the binomial, hypergeometric, and Poisson distributions. The binomial distribution describes the number of successes in a fixed number of trials when the probability of success is constant. It has applications in areas like manufacturing and marketing. The key characteristics of the binomial distribution are its mean, variance, and standard deviation. Examples are provided to demonstrate how to calculate probabilities and characteristics of the binomial distribution. Tables can also be used to find binomial probabilities.
This chapter aims to teach students how to compute and interpret various numerical descriptive measures of data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation), and shape (skewness). It covers how to find quartiles and construct box-and-whisker plots. The chapter also discusses population summary measures, rules for describing variation around the mean, and interpreting correlation coefficients.
This document provides an overview of the key topics in Chapter 6 on the normal distribution, including:
1) It introduces continuous probability distributions and defines the normal distribution as the most important continuous probability distribution.
2) It explains how the normal distribution can be standardized to have a mean of 0 and standard deviation of 1, known as the standardized normal distribution.
3) It outlines the types of problems that will be solved using the normal distribution, including finding probabilities and percentiles for both the normal and standardized normal distribution.
This document discusses the normal distribution and other continuous probability distributions. It begins by listing the learning objectives, which are to compute probabilities from the normal, uniform, exponential, and binomial distributions. It then defines continuous random variables and describes key properties of the normal distribution, including its bell shape, equal mean, median and mode, and symmetry. Several examples are provided to illustrate how to compute probabilities using the normal distribution and standardized normal table. The empirical rules for the normal distribution are also discussed.
This document provides an overview of techniques for presenting numerical data in tables and charts. It discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, polygons, ogives, bar charts, pie charts, and scatter diagrams. The chapter goals are to teach how to create and interpret these various data presentation methods using Microsoft Excel. Examples are provided for frequency distributions, histograms, polygons, and ogives to illustrate how to construct and make sense of these graphical representations of quantitative data.
This chapter introduces basic probability concepts including sample spaces, events, simple probability, joint probability, and conditional probability. It defines key terms and provides examples of calculating probabilities using contingency tables and decision trees. Probability rules are examined, including the general addition rule and rules for mutually exclusive and collectively exhaustive events. The chapter also covers statistical independence, marginal probability, and Bayes' theorem for calculating conditional probabilities.
This chapter discusses various methods for organizing and presenting data through tables and graphs. It covers techniques for categorical data like summary tables, bar charts, pie charts and Pareto diagrams. For numerical data, it discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, frequency polygons and ogives. It also introduces methods for presenting multivariate categorical data using contingency tables and side-by-side bar charts. The goal is to choose the most effective way to summarize and communicate patterns in the data.
The Normal Distribution and Other Continuous DistributionsYesica Adicondro
The document describes concepts related to the normal distribution and other continuous probability distributions. It introduces the normal distribution and its properties including that it is bell-shaped and symmetric with the mean, median and mode being equal. It describes how the mean and standard deviation determine the location and spread of the distribution. It also covers translating problems to the standardized normal distribution and how to find probabilities using the normal distribution table and by calculating the area under the normal curve.
Some Important Discrete Probability DistributionsYesica Adicondro
The chapter discusses important discrete probability distributions used in statistics for managers. It covers the binomial, hypergeometric, and Poisson distributions. The binomial distribution describes the number of successes in a fixed number of trials when the probability of success is constant. It has applications in areas like manufacturing and marketing. The key characteristics of the binomial distribution are its mean, variance, and standard deviation. Examples are provided to demonstrate how to calculate probabilities and characteristics of the binomial distribution. Tables can also be used to find binomial probabilities.
This chapter aims to teach students how to compute and interpret various numerical descriptive measures of data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation), and shape (skewness). It covers how to find quartiles and construct box-and-whisker plots. The chapter also discusses population summary measures, rules for describing variation around the mean, and interpreting correlation coefficients.
This document provides an overview of the key topics in Chapter 6 on the normal distribution, including:
1) It introduces continuous probability distributions and defines the normal distribution as the most important continuous probability distribution.
2) It explains how the normal distribution can be standardized to have a mean of 0 and standard deviation of 1, known as the standardized normal distribution.
3) It outlines the types of problems that will be solved using the normal distribution, including finding probabilities and percentiles for both the normal and standardized normal distribution.
This document discusses the normal distribution and other continuous probability distributions. It begins by listing the learning objectives, which are to compute probabilities from the normal, uniform, exponential, and binomial distributions. It then defines continuous random variables and describes key properties of the normal distribution, including its bell shape, equal mean, median and mode, and symmetry. Several examples are provided to illustrate how to compute probabilities using the normal distribution and standardized normal table. The empirical rules for the normal distribution are also discussed.
This document provides an overview of techniques for presenting numerical data in tables and charts. It discusses ordered arrays, stem-and-leaf displays, frequency distributions, histograms, polygons, ogives, bar charts, pie charts, and scatter diagrams. The chapter goals are to teach how to create and interpret these various data presentation methods using Microsoft Excel. Examples are provided for frequency distributions, histograms, polygons, and ogives to illustrate how to construct and make sense of these graphical representations of quantitative data.
This chapter discusses hypothesis testing for comparing means and variances between two populations or samples. It covers testing for the difference between two independent population means, two related (paired) population means, and two independent population variances. The key tests covered are the pooled variance t-test and separate variance t-test for independent samples, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct the hypothesis test to determine if the means or variances are significantly different.
This chapter discusses sampling and sampling distributions. The key points are:
1) A sample is a subset of a population that is used to make inferences about the population. Sampling is important because it is less time consuming and costly than a census.
2) Descriptive statistics describe samples, while inferential statistics make conclusions about populations based on sample data. Sampling distributions show the distribution of all possible values of a statistic from samples of the same size.
3) The sampling distribution of the sample mean is normally distributed for large sample sizes due to the central limit theorem. Its mean is the population mean and its standard deviation decreases with increasing sample size. Acceptance intervals can be used to determine the range a
This chapter discusses important discrete probability distributions used in business statistics. It introduces discrete random variables and their probability distributions. It defines the binomial distribution and explains how to calculate probabilities using the binomial formula. Examples are provided to demonstrate calculating the mean, variance, and covariance of discrete random variables, as well as the expected value and risk of investment portfolios. Counting techniques like combinations are also discussed for calculating binomial probabilities.
This document provides an overview of confidence interval estimation. It discusses constructing confidence intervals for the mean and proportion of a population. The chapter outlines how to determine confidence intervals when the population standard deviation is known or unknown. It also covers how to calculate the required sample size. The document uses examples and formulas to demonstrate how to establish point and interval estimates for a population parameter with a given level of confidence based on a random sample.
SPSS (Statistical Package for the Social Sciences) is software used for data analysis. It can process questionnaires, report data in tables and graphs, and analyze means, chi-squares, regression, and more. Originally its own company, SPSS is now owned by IBM and integrated into their software portfolio. The document provides an overview of using SPSS, including entering data from questionnaires, different question/response formats, and descriptive statistical analysis functions in SPSS like frequencies, cross-tabs, and graphs.
This chapter introduces basic concepts in statistics including the difference between populations and samples, parameters and statistics. It discusses the two main branches of statistics - descriptive statistics which involves collecting, summarizing and presenting data, and inferential statistics which involves drawing conclusions about populations from samples. The chapter also covers different types of data that can be collected including categorical vs. numerical, discrete vs. continuous, and different measurement scales for levels of data.
This chapter discusses important discrete probability distributions used in statistics. It begins with an introduction to discrete random variables and probability distributions. It then covers the key concepts of mean, variance, standard deviation, and covariance for discrete distributions. The chapter focuses on explaining the binomial, hypergeometric, and Poisson distributions and how to calculate probabilities using them. It concludes with examples of how to apply these distributions to areas like finance.
This chapter discusses methods for comparing two population means or proportions using statistical tests. It covers tests for independent samples, including the z-test when population variances are known and the t-test when they are unknown. It also addresses paired or related samples using a z-test when the population difference variance is known, and a t-test when it is unknown. Examples are provided for hypotheses tests and confidence intervals for the difference between two means or proportions.
This chapter discusses confidence interval estimation. It covers constructing confidence intervals for a single population mean when the population standard deviation is known or unknown, as well as confidence intervals for a single population proportion. The chapter defines key concepts like point estimates, confidence levels, and degrees of freedom. It provides examples of how to calculate confidence intervals using the normal, t, and binomial distributions and how to interpret the resulting intervals.
This chapter discusses chi-square tests and nonparametric tests. It begins by introducing contingency tables and how they are used to classify sample observations according to multiple characteristics. Examples are provided to demonstrate how to set up contingency tables and calculate expected frequencies. The chapter then explains how to perform chi-square tests to analyze differences between two or more proportions, test independence between categorical variables, and compare population medians using the Wilcoxon rank-sum test. Decision rules for each test are outlined. Worked examples are provided to demonstrate applying these statistical tests and interpreting the results.
The document discusses approximating binomial probabilities with a normal distribution. It defines the binomial distribution and states the requirements for the normal approximation are that np and nq must both be greater than or equal to 5. The normal approximation involves using a normal distribution with mean np and standard deviation npq. Examples are provided demonstrating how to calculate probabilities for binomial experiments using the normal approximation.
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
The document introduces econometrics and its methodology. Econometrics is defined as the quantitative analysis of economic phenomena based on concurrent development of economic theory and observation. It differs from economic theory, mathematics economics, and economic statistics by empirically testing economic theories. The methodology of econometrics involves: (1) stating an economic theory or hypothesis, (2) specifying its mathematical model, (3) specifying the econometric model, (4) obtaining data, (5) estimating the model, (6) testing hypotheses, (7) forecasting, and (8) using the model for policy purposes.
This chapter discusses chi-square tests and nonparametric tests. It covers chi-square tests for contingency tables to test differences between two or more proportions, including computing expected frequencies. The Marascuilo procedure is introduced for determining pairwise differences when proportions are found to be unequal. Chi-square tests of independence are discussed for contingency tables with more than two variables to test if the variables are independent. Nonparametric tests are also introduced. Examples are provided to demonstrate chi-square goodness of fit tests and tests of independence.
Chap04 discrete random variables and probability distributionJudianto Nugroho
This document provides an overview of key concepts in chapter 4 of the textbook "Statistics for Business and Economics". The chapter goals are to understand mean, standard deviation, and probability distributions for discrete random variables, including the binomial, hypergeometric, and Poisson distributions. It introduces discrete random variables and probability distributions, and defines important properties like expected value, variance, and cumulative probability functions. It also covers the Bernoulli distribution as well as the characteristics and applications of the binomial distribution.
This chapter discusses numerical descriptive measures used to describe the central tendency, variation, and shape of data. It covers calculating the mean, median, mode, variance, standard deviation, and coefficient of variation for data. The geometric mean is introduced as a measure of the average rate of change over time. Outliers are identified using z-scores. Methods for summarizing and comparing data using these descriptive statistics are presented.
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
1. The document discusses the nature of regression analysis, which involves studying the dependence of a dependent variable on one or more explanatory variables, with the goal of estimating or predicting the average value of the dependent variable based on the explanatory variables.
2. It provides examples of regression analysis, such as studying how crop yield depends on factors like temperature, rainfall, and fertilizer. It also distinguishes between statistical and deterministic relationships, and notes that regression analysis indicates dependence but does not necessarily imply causation.
3. Regression analysis differs from correlation analysis in that it treats the dependent and explanatory variables asymmetrically, with the goal of prediction rather than just measuring the strength of the linear association between variables.
This document outlines the key goals and concepts covered in Chapter 6 of the textbook "Statistics for Managers Using Microsoft Excel". The chapter introduces continuous probability distributions, including the normal, uniform, and exponential distributions. It describes the characteristics of the normal distribution and how to translate problems into standardized normal distribution problems. The chapter also covers sampling distributions, the central limit theorem, and how to find probabilities using the normal distribution table.
This document provides an overview of sampling and sampling distributions. It begins by stating the chapter goals, which are to describe key sampling concepts like simple random samples and explain the differences between descriptive and inferential statistics. It then defines important terms like population, sample, and sampling distribution. The document explains that sampling is used instead of censuses because it is less time-consuming and costly while still providing sufficiently precise results. It also outlines the chapter, noting it will cover the sampling distributions of the sample mean, sample proportion, and sample variance. It provides examples of how to determine the properties of these sampling distributions such as their means and standard deviations. It emphasizes the central limit theorem and how large samples lead to normally distributed sampling distributions even
This document provides an overview of sampling and sampling distributions. It defines key concepts like populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains how sampling distributions are developed and their properties. Specifically, it discusses the sampling distribution of the sample mean, including how it has an expected value equal to the population mean and standard error that decreases as sample size increases. The Central Limit Theorem is also summarized, stating that as sample size increases, the sampling distribution will approach a normal distribution regardless of the shape of the original population.
This chapter discusses hypothesis testing for comparing means and variances between two populations or samples. It covers testing for the difference between two independent population means, two related (paired) population means, and two independent population variances. The key tests covered are the pooled variance t-test and separate variance t-test for independent samples, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct the hypothesis test to determine if the means or variances are significantly different.
This chapter discusses sampling and sampling distributions. The key points are:
1) A sample is a subset of a population that is used to make inferences about the population. Sampling is important because it is less time consuming and costly than a census.
2) Descriptive statistics describe samples, while inferential statistics make conclusions about populations based on sample data. Sampling distributions show the distribution of all possible values of a statistic from samples of the same size.
3) The sampling distribution of the sample mean is normally distributed for large sample sizes due to the central limit theorem. Its mean is the population mean and its standard deviation decreases with increasing sample size. Acceptance intervals can be used to determine the range a
This chapter discusses important discrete probability distributions used in business statistics. It introduces discrete random variables and their probability distributions. It defines the binomial distribution and explains how to calculate probabilities using the binomial formula. Examples are provided to demonstrate calculating the mean, variance, and covariance of discrete random variables, as well as the expected value and risk of investment portfolios. Counting techniques like combinations are also discussed for calculating binomial probabilities.
This document provides an overview of confidence interval estimation. It discusses constructing confidence intervals for the mean and proportion of a population. The chapter outlines how to determine confidence intervals when the population standard deviation is known or unknown. It also covers how to calculate the required sample size. The document uses examples and formulas to demonstrate how to establish point and interval estimates for a population parameter with a given level of confidence based on a random sample.
SPSS (Statistical Package for the Social Sciences) is software used for data analysis. It can process questionnaires, report data in tables and graphs, and analyze means, chi-squares, regression, and more. Originally its own company, SPSS is now owned by IBM and integrated into their software portfolio. The document provides an overview of using SPSS, including entering data from questionnaires, different question/response formats, and descriptive statistical analysis functions in SPSS like frequencies, cross-tabs, and graphs.
This chapter introduces basic concepts in statistics including the difference between populations and samples, parameters and statistics. It discusses the two main branches of statistics - descriptive statistics which involves collecting, summarizing and presenting data, and inferential statistics which involves drawing conclusions about populations from samples. The chapter also covers different types of data that can be collected including categorical vs. numerical, discrete vs. continuous, and different measurement scales for levels of data.
This chapter discusses important discrete probability distributions used in statistics. It begins with an introduction to discrete random variables and probability distributions. It then covers the key concepts of mean, variance, standard deviation, and covariance for discrete distributions. The chapter focuses on explaining the binomial, hypergeometric, and Poisson distributions and how to calculate probabilities using them. It concludes with examples of how to apply these distributions to areas like finance.
This chapter discusses methods for comparing two population means or proportions using statistical tests. It covers tests for independent samples, including the z-test when population variances are known and the t-test when they are unknown. It also addresses paired or related samples using a z-test when the population difference variance is known, and a t-test when it is unknown. Examples are provided for hypotheses tests and confidence intervals for the difference between two means or proportions.
This chapter discusses confidence interval estimation. It covers constructing confidence intervals for a single population mean when the population standard deviation is known or unknown, as well as confidence intervals for a single population proportion. The chapter defines key concepts like point estimates, confidence levels, and degrees of freedom. It provides examples of how to calculate confidence intervals using the normal, t, and binomial distributions and how to interpret the resulting intervals.
This chapter discusses chi-square tests and nonparametric tests. It begins by introducing contingency tables and how they are used to classify sample observations according to multiple characteristics. Examples are provided to demonstrate how to set up contingency tables and calculate expected frequencies. The chapter then explains how to perform chi-square tests to analyze differences between two or more proportions, test independence between categorical variables, and compare population medians using the Wilcoxon rank-sum test. Decision rules for each test are outlined. Worked examples are provided to demonstrate applying these statistical tests and interpreting the results.
The document discusses approximating binomial probabilities with a normal distribution. It defines the binomial distribution and states the requirements for the normal approximation are that np and nq must both be greater than or equal to 5. The normal approximation involves using a normal distribution with mean np and standard deviation npq. Examples are provided demonstrating how to calculate probabilities for binomial experiments using the normal approximation.
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
The document introduces econometrics and its methodology. Econometrics is defined as the quantitative analysis of economic phenomena based on concurrent development of economic theory and observation. It differs from economic theory, mathematics economics, and economic statistics by empirically testing economic theories. The methodology of econometrics involves: (1) stating an economic theory or hypothesis, (2) specifying its mathematical model, (3) specifying the econometric model, (4) obtaining data, (5) estimating the model, (6) testing hypotheses, (7) forecasting, and (8) using the model for policy purposes.
This chapter discusses chi-square tests and nonparametric tests. It covers chi-square tests for contingency tables to test differences between two or more proportions, including computing expected frequencies. The Marascuilo procedure is introduced for determining pairwise differences when proportions are found to be unequal. Chi-square tests of independence are discussed for contingency tables with more than two variables to test if the variables are independent. Nonparametric tests are also introduced. Examples are provided to demonstrate chi-square goodness of fit tests and tests of independence.
Chap04 discrete random variables and probability distributionJudianto Nugroho
This document provides an overview of key concepts in chapter 4 of the textbook "Statistics for Business and Economics". The chapter goals are to understand mean, standard deviation, and probability distributions for discrete random variables, including the binomial, hypergeometric, and Poisson distributions. It introduces discrete random variables and probability distributions, and defines important properties like expected value, variance, and cumulative probability functions. It also covers the Bernoulli distribution as well as the characteristics and applications of the binomial distribution.
This chapter discusses numerical descriptive measures used to describe the central tendency, variation, and shape of data. It covers calculating the mean, median, mode, variance, standard deviation, and coefficient of variation for data. The geometric mean is introduced as a measure of the average rate of change over time. Outliers are identified using z-scores. Methods for summarizing and comparing data using these descriptive statistics are presented.
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
1. The document discusses the nature of regression analysis, which involves studying the dependence of a dependent variable on one or more explanatory variables, with the goal of estimating or predicting the average value of the dependent variable based on the explanatory variables.
2. It provides examples of regression analysis, such as studying how crop yield depends on factors like temperature, rainfall, and fertilizer. It also distinguishes between statistical and deterministic relationships, and notes that regression analysis indicates dependence but does not necessarily imply causation.
3. Regression analysis differs from correlation analysis in that it treats the dependent and explanatory variables asymmetrically, with the goal of prediction rather than just measuring the strength of the linear association between variables.
This document outlines the key goals and concepts covered in Chapter 6 of the textbook "Statistics for Managers Using Microsoft Excel". The chapter introduces continuous probability distributions, including the normal, uniform, and exponential distributions. It describes the characteristics of the normal distribution and how to translate problems into standardized normal distribution problems. The chapter also covers sampling distributions, the central limit theorem, and how to find probabilities using the normal distribution table.
This document provides an overview of sampling and sampling distributions. It begins by stating the chapter goals, which are to describe key sampling concepts like simple random samples and explain the differences between descriptive and inferential statistics. It then defines important terms like population, sample, and sampling distribution. The document explains that sampling is used instead of censuses because it is less time-consuming and costly while still providing sufficiently precise results. It also outlines the chapter, noting it will cover the sampling distributions of the sample mean, sample proportion, and sample variance. It provides examples of how to determine the properties of these sampling distributions such as their means and standard deviations. It emphasizes the central limit theorem and how large samples lead to normally distributed sampling distributions even
This document provides an overview of sampling and sampling distributions. It defines key concepts like populations, samples, descriptive statistics, inferential statistics, and simple random samples. It explains how sampling distributions are developed and their properties. Specifically, it discusses the sampling distribution of the sample mean, including how it has an expected value equal to the population mean and standard error that decreases as sample size increases. The Central Limit Theorem is also summarized, stating that as sample size increases, the sampling distribution will approach a normal distribution regardless of the shape of the original population.
This chapter discusses sampling distributions and their properties. It covers the sampling distribution of the mean and the proportion. The key points are:
- A sampling distribution describes the distribution of a statistic like the mean from random samples of a population.
- The Central Limit Theorem states that as sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normal.
- For the mean, the sampling distribution has a mean equal to the population mean and standard deviation that decreases as sample size increases.
- For a proportion, the sampling distribution can be approximated as normal if sample size n and np or n(1-p) are large enough.
This chapter discusses additional topics in sampling, including:
- The basic steps of a sampling study and types of sampling errors
- Methods such as simple random sampling, stratified sampling, and estimating population parameters like the mean, total, and proportion from samples
- How to determine sample sizes and construct confidence intervals for estimating population values
- Other sampling methods like cluster sampling and non-probability samples are also introduced.
This chapter introduces key concepts in statistics. It explains that business decisions are often made with incomplete information due to uncertainty. It defines important terms like population, sample, parameter, and statistic. Descriptive statistics are used to collect and summarize data, while inferential statistics allow predictions and estimates to transform information into knowledge. The goal is for students to understand how statistics helps inform business decision making.
This chapter discusses sampling and sampling distributions. It defines key sampling concepts like the sampling frame, population, and different sampling methods including probability and non-probability samples. Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. The chapter also covers sampling distributions and how the distribution of sample means approaches a normal distribution as the sample size increases due to the Central Limit Theorem, even if the population is not normally distributed. This allows inferring properties of the population from a sample.
This chapter discusses various numerical descriptive statistics used to describe data, including measures of central tendency (mean, median, mode), variation (range, standard deviation, variance), and the shape of distributions. It covers how to calculate and interpret these statistics, and explains how they are used to summarize and analyze sample data. The chapter objectives are to be able to compute and understand the meaning of common descriptive statistics, and know how and when to apply them appropriately.
business statistics . In this chapter, you learn:
To construct and interpret confidence interval estimates for the population mean
To determine the sample size necessary to develop a confidence interval for the population mean
A point estimate is a single number,
a confidence interval provides additional information about the variability of the estimate
Suppose confidence level = 95%
Also written (1 - ) = 0.95, (so = 0.05)
A relative frequency interpretation:
95% of all the confidence intervals that can be constructed will contain the unknown true parameter
A specific interval either will contain or will not contain the true parameter
No probability involved in a specific interval. A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
Determine a 95% confidence interval for the true mean resistance of the population.
A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.
We are 95% confident that the true mean resistance is between 1.9932 and 2.4068 ohms
Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean
Interpreting this interval requires the assumption that the population you are sampling from is approximately a normal distribution (especially since n is only 25).
This condition can be checked by creating a:
Normal probability plot or
Boxplot
The required sample size can be found to reach a desired margin of error (e) with a specified level of confidence (1 - )
The margin of error is also called sampling error
the amount of imprecision in the estimate of the population parameter
the amount added and subtracted to the point estimate to form the confidence interval
This document provides an overview of sampling distributions and the central limit theorem. It begins with definitions of key terms like population, sample, and sampling distribution. It then demonstrates how to develop a sampling distribution by considering all possible samples from a population. The document explains that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, even if the population is not normally distributed, according to the central limit theorem. It provides examples of how to calculate probabilities related to sampling distributions.
This chapter discusses additional topics related to estimation, including forming confidence intervals for differences between dependent and independent population means and proportions. It provides formulas and examples for confidence intervals when population variances are known or unknown, and when variances are assumed equal or unequal. The chapter goals are to enable readers to compute confidence intervals and determine sample sizes for a variety of estimation problems involving means, proportions, differences between populations, and variances.
This chapter introduces statistics concepts for business and economics. It explains that decisions are often made with incomplete information due to uncertainty. Key terms are defined, including population, sample, parameter, and statistic. Random sampling is described as a procedure where each member of a population has an equal chance of being selected. The two main branches of statistics - descriptive and inferential - are examined. Descriptive statistics involves collecting and summarizing data, while inferential statistics allows for predictions, estimates, and hypothesis testing based on sample results. The decision making process is reviewed as moving from identifying a problem to collecting data, transforming it into information and knowledge, and making a decision.
This chapter discusses methods for constructing confidence intervals for differences and comparisons between population parameters using sample data. It covers constructing confidence intervals for the difference between two independent population means when the standard deviations are known or unknown. It also addresses constructing confidence intervals when the population variances are assumed to be equal or unequal. The chapter concludes with constructing confidence intervals for the difference between two independent population proportions.
Sampling distributions stat ppt @ bec domsBabasab Patil
The document discusses sampling distributions and their properties. It defines sampling error and how to calculate it. It explains that the sampling distribution of the sample mean x is normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. Similarly, the sampling distribution of the sample proportion p is normally distributed when the sample size is large. The Central Limit Theorem states that the sampling distribution will be approximately normal for large sample sizes regardless of the population distribution.
This chapter discusses analysis of variance (ANOVA) techniques. It covers one-way and two-way ANOVA designs, and how to perform and interpret one-way and two-way ANOVA tests. It also discusses the Kruskal-Wallis test, which can be used as a non-parametric alternative to one-way ANOVA when the normality assumption is violated. The chapter provides examples of partitioning variability into within-group and between-group components, calculating test statistics like F ratios, and interpreting the results of one-way ANOVA analyses to determine if population means are equal or different.
- Univariate analysis refers to analyzing one variable at a time using statistical measures like proportions, percentages, means, medians, and modes to describe data.
- These measures provide a "snapshot" of a variable through tools like frequency tables and charts to understand patterns and the distribution of cases.
- Measures of central tendency like the mean, median and mode indicate typical or average values, while measures of dispersion like the standard deviation and range indicate how spread out or varied the data are around central values.
This chapter discusses sampling and sampling distributions. It covers different sampling methods like simple random sampling, stratified sampling, and cluster sampling. The key concepts explained are sampling frame, sampling distribution, standard error of the mean, and the Central Limit Theorem. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean will approach a normal distribution, even if the population is not normally distributed.
This chapter discusses probability distributions used in statistics. It introduces the normal, uniform, and exponential distributions and explains how to calculate probabilities using each. It also covers sampling distributions and how the mean and standard deviation are used to describe sampling distributions for both the sample mean and proportion. The central limit theorem is introduced along with how it is important and how sampling distributions can be applied.
This chapter discusses nonparametric statistical tests that make fewer assumptions about the underlying data distribution, including the sign test, Wilcoxon signed-rank test, and Mann-Whitney U-test. It provides examples of how to conduct each test and interpret the results. The sign test can test for differences in paired samples or a single population median. The Wilcoxon signed-rank test incorporates information about the magnitude of differences between paired samples. The Mann-Whitney U-test compares two independent samples and tests whether their population medians are the same.
This chapter discusses confidence intervals for estimating population parameters. It covers confidence intervals for the mean when the population variance is known and unknown, and for the population proportion. The chapter defines point and interval estimates, and unbiasedness, consistency, and efficiency of estimators. It presents the general formula for confidence intervals and how to calculate reliability factors using the normal and t-distributions. Examples are provided to demonstrate constructing confidence intervals for a population mean.
This chapter discusses hypothesis testing, which involves formulating a null hypothesis (H0) and an alternative hypothesis (H1) about a population parameter, collecting a sample, and determining whether to reject the null hypothesis based on the sample data. The key points covered are:
- H0 states the assumption to be tested numerically, while H1 challenges the status quo.
- Type I and Type II errors can occur depending on whether H0 is correctly rejected or not rejected.
- Hypothesis tests for a mean can use a z-test if the population standard deviation is known, or a t-test if it is unknown.
- The significance level, critical values, and p-values are used
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptxgoluk9330
Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
PPT on Direct Seeded Rice presented at the three-day 'Training and Validation Workshop on Modules of Climate Smart Agriculture (CSA) Technologies in South Asia' workshop on April 22, 2024.
Signatures of wave erosion in Titan’s coastsSérgio Sacani
The shorelines of Titan’s hydrocarbon seas trace flooded erosional landforms such as river valleys; however, it isunclear whether coastal erosion has subsequently altered these shorelines. Spacecraft observations and theo-retical models suggest that wind may cause waves to form on Titan’s seas, potentially driving coastal erosion,but the observational evidence of waves is indirect, and the processes affecting shoreline evolution on Titanremain unknown. No widely accepted framework exists for using shoreline morphology to quantitatively dis-cern coastal erosion mechanisms, even on Earth, where the dominant mechanisms are known. We combinelandscape evolution models with measurements of shoreline shape on Earth to characterize how differentcoastal erosion mechanisms affect shoreline morphology. Applying this framework to Titan, we find that theshorelines of Titan’s seas are most consistent with flooded landscapes that subsequently have been eroded bywaves, rather than a uniform erosional process or no coastal erosion, particularly if wave growth saturates atfetch lengths of tens of kilometers.
PPT on Alternate Wetting and Drying presented at the three-day 'Training and Validation Workshop on Modules of Climate Smart Agriculture (CSA) Technologies in South Asia' workshop on April 22, 2024.
Sexuality - Issues, Attitude and Behaviour - Applied Social Psychology - Psyc...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDSSérgio Sacani
The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both light and heavy seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between light and heavy seeds with light at one end and heavy at the other that instead a continuum exists. Light seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the heaviest seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that light seeds must be at least 103 to 105 times more numerous than heavy seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes heavy seeds (Mseed > 103 M⊙) a significantly more likely pathway given that heavy seeds have an abundance pattern than is close to and likely in excess of 10−4 compared to light seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.