This document discusses hypothesis testing, including:
- The chapter introduces hypothesis testing and defines key concepts like the null hypothesis, alternative hypothesis, type I and type II errors, and significance levels.
- It explains how to formulate and test hypotheses about population means and proportions, including how to determine critical values and p-values.
- The steps of hypothesis testing are outlined, and an example is provided to demonstrate how to test a claim about a population mean using a z-test.
- Both critical value and p-value approaches to testing hypotheses are described.
This chapter discusses fundamentals of hypothesis testing for one-sample tests. It covers:
1) Formulating the null and alternative hypotheses for tests involving a single population mean or proportion.
2) Using critical value and p-value approaches to test the null hypothesis, and defining Type I and Type II errors.
3) How to perform hypothesis tests for a single population mean when the population standard deviation is known or unknown.
This chapter discusses the fundamentals of hypothesis testing for one-sample tests. It introduces the concepts of the null hypothesis (H0), alternative hypothesis (H1), test statistic, critical values, significance level, Type I and Type II errors. It explains the hypothesis testing process and covers the z-test and t-test for comparing a sample mean to a hypothesized population mean. An example demonstrates a two-tailed t-test to determine if there is evidence that the average cost of hotel rooms in New York is different than the claimed mean of $168, finding insufficient evidence based on a sample.
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.
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.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
This chapter discusses two-sample tests, including tests for the difference between two independent population means, the difference between two related (paired) sample means, the difference between two population proportions, and the difference between two variances. It provides the formulas and procedures for conducting Z tests, t tests, and F tests for these comparisons in situations where the population standard deviations are both known and unknown. The goal is to test hypotheses about differences between parameters of two populations or to construct confidence intervals for these differences.
1. The document discusses techniques for using the chi-square distribution to test hypotheses, including goodness-of-fit tests to compare observed and expected frequencies and contingency table analysis to test for relationships between categorical variables.
2. Examples are provided to demonstrate how to conduct chi-square tests, including stating hypotheses, selecting test statistics, computing expected frequencies, and determining whether to reject the null hypothesis.
3. One example analyzes survey data on hospital admissions of seniors to determine if it is consistent with national data, while another uses data on ex-prisoners' adjustments to test for a relationship between adjustment and living location. Both examples compute chi-square statistics that do not reject the null hypotheses.
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
Chapter Topic:
Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
Potential Hypothesis-Testing Pitfalls and Ethical Issues
This chapter discusses fundamentals of hypothesis testing for one-sample tests. It covers:
1) Formulating the null and alternative hypotheses for tests involving a single population mean or proportion.
2) Using critical value and p-value approaches to test the null hypothesis, and defining Type I and Type II errors.
3) How to perform hypothesis tests for a single population mean when the population standard deviation is known or unknown.
This chapter discusses the fundamentals of hypothesis testing for one-sample tests. It introduces the concepts of the null hypothesis (H0), alternative hypothesis (H1), test statistic, critical values, significance level, Type I and Type II errors. It explains the hypothesis testing process and covers the z-test and t-test for comparing a sample mean to a hypothesized population mean. An example demonstrates a two-tailed t-test to determine if there is evidence that the average cost of hotel rooms in New York is different than the claimed mean of $168, finding insufficient evidence based on a sample.
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.
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.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
This chapter discusses two-sample tests, including tests for the difference between two independent population means, the difference between two related (paired) sample means, the difference between two population proportions, and the difference between two variances. It provides the formulas and procedures for conducting Z tests, t tests, and F tests for these comparisons in situations where the population standard deviations are both known and unknown. The goal is to test hypotheses about differences between parameters of two populations or to construct confidence intervals for these differences.
1. The document discusses techniques for using the chi-square distribution to test hypotheses, including goodness-of-fit tests to compare observed and expected frequencies and contingency table analysis to test for relationships between categorical variables.
2. Examples are provided to demonstrate how to conduct chi-square tests, including stating hypotheses, selecting test statistics, computing expected frequencies, and determining whether to reject the null hypothesis.
3. One example analyzes survey data on hospital admissions of seniors to determine if it is consistent with national data, while another uses data on ex-prisoners' adjustments to test for a relationship between adjustment and living location. Both examples compute chi-square statistics that do not reject the null hypotheses.
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
Chapter Topic:
Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
Potential Hypothesis-Testing Pitfalls and Ethical Issues
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.
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.
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 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 confidence interval estimation for means and proportions. It introduces key concepts such as point estimates, confidence intervals, and confidence levels. For a mean where the population standard deviation is known, the confidence interval formula uses the normal distribution. When the standard deviation is unknown, the t-distribution is used instead. For a proportion, the confidence interval adds an allowance for uncertainty to the sample proportion. The chapter also covers determining sample sizes and interpreting confidence intervals.
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.
This chapter discusses two-sample hypothesis tests for comparing population means and proportions between two independent samples, and between two related samples. It introduces tests for comparing the means of two independent populations, two related populations, and the proportions of two independent populations. The key tests covered are the pooled variance t-test for independent samples with equal variances, separate variance t-test for independent samples with unequal variances, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct hypothesis tests to compare sample means and determine if they are statistically different. Confidence intervals for the difference between two means are also discussed.
The document provides an overview of analysis of variance (ANOVA) techniques, including:
- One-way ANOVA to evaluate differences between three or more group means and the assumptions of one-way ANOVA.
- Partitioning total variation into between-group and within-group components.
- Computing test statistics like the F-ratio to test for differences between group means.
- Interpreting one-way ANOVA results including rejecting the null hypothesis of no difference between means.
- An example one-way ANOVA calculation and interpretation using golf club distance data.
Hypothesis testing refers to formal statistical procedures used to accept or reject claims about populations based on data. It involves:
1) Stating a null hypothesis that makes a claim about a population parameter.
2) Collecting sample data and computing a test statistic.
3) Determining whether to reject the null hypothesis based on the probability of obtaining the sample statistic if the null is true.
Rejecting the null supports the alternative hypothesis. Type I and Type II errors occur when the null is incorrectly rejected or not rejected. Hypothesis tests aim to minimize errors while maximizing power to detect meaningful alternative hypotheses.
This document discusses various numerical descriptive techniques used for summarizing and describing quantitative data, including:
- Measures of central location (mean, median, mode) and how to calculate them
- Measures of variability (range, variance, standard deviation) and how they are used to quantify the dispersion of data around the mean
- Other concepts like percentiles, the empirical rule, Chebyshev's theorem, and box plots. Examples are provided to illustrate how to apply these techniques to sample data sets.
This document discusses one-sample hypothesis tests. It defines key terms like hypotheses, null and alternative hypotheses, Type I and Type II errors, test statistics, critical values, one-tailed and two-tailed tests. It provides examples of how to set up and conduct hypothesis tests to analyze a population mean. This includes situations when the population standard deviation is known or unknown. The examples show how to state the hypotheses, select the significance level, identify the appropriate test statistic, determine the decision rule, and make a conclusion.
This document provides an overview of key concepts related to the normal distribution, sampling distributions, estimation, and hypothesis testing. It defines important terms like the normal curve, z-scores, sampling distributions, point and interval estimates, and the steps of hypothesis testing including stating hypotheses, collecting data, and determining whether to reject the null hypothesis. It also reviews concepts like the central limit theorem, standard error, bias, confidence intervals, types of errors in hypothesis testing, and factors that influence test statistics.
This chapter discusses two-sample hypothesis tests for comparing means and proportions between two independent populations or between paired/dependent samples. It provides examples of hypothesis tests to compare the means of two independent samples using the z-test if populations are normal and sample sizes are large, or the t-test if populations are normal but sample sizes are small. Tests are also shown to compare proportions between two independent populations using the z-test, and to compare means between paired samples using the t-test.
This document summarizes the key topics and concepts covered in Chapter 2 of the 9th edition of the business statistics textbook "Presenting Data in Tables and Charts". The chapter discusses guidelines for analyzing data and organizing both numerical and categorical data. It then covers various methods for tabulating and graphing univariate and bivariate data, including tables, histograms, frequency distributions, scatter plots, bar charts, pie charts, and contingency tables.
- Hypothesis testing involves evaluating claims about population parameters by comparing a null hypothesis to an alternative hypothesis.
- The null hypothesis states that there is no difference or effect, while the alternative hypothesis states that a difference or effect exists.
- There are three main methods for hypothesis testing: the critical value method which separates a critical region from a noncritical region, the p-value method which calculates the probability of obtaining a test statistic at least as extreme as the sample test statistic assuming the null is true, and the confidence interval method which rejects claims not included in the confidence interval.
- The steps of hypothesis testing are to state the hypotheses, calculate the test statistic, find the critical value, make a decision to reject
This document discusses using one-way ANOVA in SPSS to compare mean salaries among employee age groups. It finds a significant difference in monthly salaries between the three age groups. Post hoc tests show that all three group means are significantly different from one another. Two other examples are presented: the first finds no significant difference in the importance of growth and development between age groups, while the second does find a significant difference in the importance of a safe work environment between the youngest and oldest age groups specifically.
Basic Business Statistics Chapter 3Numerical Descriptive Measures
Chapters Objectives:
Learn about Measures of Center.
How to calculate mean, median and midrange
Learn about Measures of Spread
Learn how to calculate Standard Deviation, IQR and Range
Learn about 5 number summaries
Coefficient of Correlation
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 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 chapter discusses fundamentals of hypothesis testing for one-sample tests. It introduces key concepts like the null and alternative hypotheses, type I and type II errors, and p-value approach. It provides examples of hypothesis testing for a population mean using a one-sample t-test when the population standard deviation is both known and unknown. It also discusses hypothesis testing for a population proportion using a one-sample z-test. The chapter outlines the steps to conduct hypothesis testing and interprets the conclusions.
Hypothesis Test _One-sample t-test, Z-test, Proportion Z-testRavindra Nath Shukla
This document discusses hypothesis testing concepts including the null and alternative hypotheses, type I and II errors, and the hypothesis testing process. It provides examples of hypothesis testing for a mean where the population standard deviation is known (z-test) and unknown (t-test). The document outlines the 6 steps in hypothesis testing and provides examples using both the critical value approach and p-value approach. It discusses the relationship between hypothesis testing and confidence intervals.
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.
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.
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 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 confidence interval estimation for means and proportions. It introduces key concepts such as point estimates, confidence intervals, and confidence levels. For a mean where the population standard deviation is known, the confidence interval formula uses the normal distribution. When the standard deviation is unknown, the t-distribution is used instead. For a proportion, the confidence interval adds an allowance for uncertainty to the sample proportion. The chapter also covers determining sample sizes and interpreting confidence intervals.
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.
This chapter discusses two-sample hypothesis tests for comparing population means and proportions between two independent samples, and between two related samples. It introduces tests for comparing the means of two independent populations, two related populations, and the proportions of two independent populations. The key tests covered are the pooled variance t-test for independent samples with equal variances, separate variance t-test for independent samples with unequal variances, and the paired t-test for related samples. Examples are provided to demonstrate how to calculate the test statistic and conduct hypothesis tests to compare sample means and determine if they are statistically different. Confidence intervals for the difference between two means are also discussed.
The document provides an overview of analysis of variance (ANOVA) techniques, including:
- One-way ANOVA to evaluate differences between three or more group means and the assumptions of one-way ANOVA.
- Partitioning total variation into between-group and within-group components.
- Computing test statistics like the F-ratio to test for differences between group means.
- Interpreting one-way ANOVA results including rejecting the null hypothesis of no difference between means.
- An example one-way ANOVA calculation and interpretation using golf club distance data.
Hypothesis testing refers to formal statistical procedures used to accept or reject claims about populations based on data. It involves:
1) Stating a null hypothesis that makes a claim about a population parameter.
2) Collecting sample data and computing a test statistic.
3) Determining whether to reject the null hypothesis based on the probability of obtaining the sample statistic if the null is true.
Rejecting the null supports the alternative hypothesis. Type I and Type II errors occur when the null is incorrectly rejected or not rejected. Hypothesis tests aim to minimize errors while maximizing power to detect meaningful alternative hypotheses.
This document discusses various numerical descriptive techniques used for summarizing and describing quantitative data, including:
- Measures of central location (mean, median, mode) and how to calculate them
- Measures of variability (range, variance, standard deviation) and how they are used to quantify the dispersion of data around the mean
- Other concepts like percentiles, the empirical rule, Chebyshev's theorem, and box plots. Examples are provided to illustrate how to apply these techniques to sample data sets.
This document discusses one-sample hypothesis tests. It defines key terms like hypotheses, null and alternative hypotheses, Type I and Type II errors, test statistics, critical values, one-tailed and two-tailed tests. It provides examples of how to set up and conduct hypothesis tests to analyze a population mean. This includes situations when the population standard deviation is known or unknown. The examples show how to state the hypotheses, select the significance level, identify the appropriate test statistic, determine the decision rule, and make a conclusion.
This document provides an overview of key concepts related to the normal distribution, sampling distributions, estimation, and hypothesis testing. It defines important terms like the normal curve, z-scores, sampling distributions, point and interval estimates, and the steps of hypothesis testing including stating hypotheses, collecting data, and determining whether to reject the null hypothesis. It also reviews concepts like the central limit theorem, standard error, bias, confidence intervals, types of errors in hypothesis testing, and factors that influence test statistics.
This chapter discusses two-sample hypothesis tests for comparing means and proportions between two independent populations or between paired/dependent samples. It provides examples of hypothesis tests to compare the means of two independent samples using the z-test if populations are normal and sample sizes are large, or the t-test if populations are normal but sample sizes are small. Tests are also shown to compare proportions between two independent populations using the z-test, and to compare means between paired samples using the t-test.
This document summarizes the key topics and concepts covered in Chapter 2 of the 9th edition of the business statistics textbook "Presenting Data in Tables and Charts". The chapter discusses guidelines for analyzing data and organizing both numerical and categorical data. It then covers various methods for tabulating and graphing univariate and bivariate data, including tables, histograms, frequency distributions, scatter plots, bar charts, pie charts, and contingency tables.
- Hypothesis testing involves evaluating claims about population parameters by comparing a null hypothesis to an alternative hypothesis.
- The null hypothesis states that there is no difference or effect, while the alternative hypothesis states that a difference or effect exists.
- There are three main methods for hypothesis testing: the critical value method which separates a critical region from a noncritical region, the p-value method which calculates the probability of obtaining a test statistic at least as extreme as the sample test statistic assuming the null is true, and the confidence interval method which rejects claims not included in the confidence interval.
- The steps of hypothesis testing are to state the hypotheses, calculate the test statistic, find the critical value, make a decision to reject
This document discusses using one-way ANOVA in SPSS to compare mean salaries among employee age groups. It finds a significant difference in monthly salaries between the three age groups. Post hoc tests show that all three group means are significantly different from one another. Two other examples are presented: the first finds no significant difference in the importance of growth and development between age groups, while the second does find a significant difference in the importance of a safe work environment between the youngest and oldest age groups specifically.
Basic Business Statistics Chapter 3Numerical Descriptive Measures
Chapters Objectives:
Learn about Measures of Center.
How to calculate mean, median and midrange
Learn about Measures of Spread
Learn how to calculate Standard Deviation, IQR and Range
Learn about 5 number summaries
Coefficient of Correlation
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 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 chapter discusses fundamentals of hypothesis testing for one-sample tests. It introduces key concepts like the null and alternative hypotheses, type I and type II errors, and p-value approach. It provides examples of hypothesis testing for a population mean using a one-sample t-test when the population standard deviation is both known and unknown. It also discusses hypothesis testing for a population proportion using a one-sample z-test. The chapter outlines the steps to conduct hypothesis testing and interprets the conclusions.
Hypothesis Test _One-sample t-test, Z-test, Proportion Z-testRavindra Nath Shukla
This document discusses hypothesis testing concepts including the null and alternative hypotheses, type I and II errors, and the hypothesis testing process. It provides examples of hypothesis testing for a mean where the population standard deviation is known (z-test) and unknown (t-test). The document outlines the 6 steps in hypothesis testing and provides examples using both the critical value approach and p-value approach. It discusses the relationship between hypothesis testing and confidence intervals.
IN ORDER TO IMPLEMENT A SET OF RULES / TUTORIALOUTLET DOT COMjorge0050
Solve each trigonometric equation in the interval [0,2n) by first squaring both sides. fleas x=1+sin x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A- The solution set is .
(Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using 1: as needed. Use integers or fractions for any numbers in the expression.) 0 B. There is no solution on this interval.
This chapter discusses various numerical descriptive measures that can be used to describe and analyze data. It covers measures of central tendency like the mean, median, and mode. It also discusses measures of variation such as the range, variance, standard deviation, and coefficient of variation. Other topics covered include quartiles, the empirical rule, box-and-whisker plots, correlation coefficients, and choosing the appropriate descriptive measure based on the characteristics of the data. The goals are to help readers compute and interpret these common statistical measures, and use them together with graphs and charts to describe and analyze data.
This document provides an overview of one-sample hypothesis tests. It defines key terms related to hypothesis testing such as the null and alternative hypotheses, test statistic, critical value, Type I and Type II errors, and p-value. It explains the five-step hypothesis testing procedure and how to set up hypotheses for tests involving a population mean or proportion. Examples are provided to demonstrate how to conduct hypothesis tests about a population mean when the population standard deviation is known or unknown, and how to conduct a test about a population proportion. The document also discusses how to interpret p-values and the concept of Type II errors.
This document provides an overview of hypothesis testing concepts including:
- A hypothesis is a claim about a population parameter that can be tested statistically. The null hypothesis states the claim to be tested, while the alternative hypothesis is what the researcher is trying to prove.
- The level of significance and critical values determine the rejection region where the null hypothesis would be rejected. Type I and Type II errors refer to incorrectly rejecting or failing to reject the null hypothesis.
- The key steps of hypothesis testing are stated as: 1) specify null and alternative hypotheses, 2) choose significance level and sample size, 3) determine test statistic, 4) find critical values, 5) collect data and compute test statistic, 6) make a decision
Introduction to hypothesis testing ppt @ bec domsBabasab Patil
This document introduces hypothesis testing, including:
- Formulating null and alternative hypotheses for tests involving population means and proportions
- Using test statistics, critical values, and p-values to test hypotheses
- Defining Type I and Type II errors and their probabilities
- Examples of hypothesis tests for means (using z-tests and t-tests) and proportions (using z-tests) are provided to illustrate the concepts.
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 document provides an overview of hypothesis testing. It defines key terms like the null hypothesis (H0), alternative hypothesis (H1), type I and type II errors, significance level, p-values, and test statistics. It explains the basic steps in hypothesis testing as testing a claim about a population parameter by collecting a sample, determining the appropriate test statistic based on the sampling distribution, and comparing it to critical values to reject or fail to reject the null hypothesis. Examples are provided to demonstrate hypothesis tests for a mean when the population standard deviation is known or unknown.
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 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 confidence interval estimation. It defines point estimates and confidence intervals, and explains how to construct confidence intervals for a population mean when the population standard deviation is known or unknown, as well as for a population proportion. When the population standard deviation is unknown, a t-distribution rather than normal distribution is used. Formulas and examples are provided. The chapter also addresses determining the required sample size to estimate a mean or proportion within a specified margin of error.
1. The document discusses the basic principles of hypothesis testing, including stating the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining critical values, and making a decision to reject or fail to reject the null hypothesis.
2. It outlines the five steps of hypothesis testing: state hypotheses, select significance level, select test statistic, determine critical value, and make a decision.
3. Key terms discussed include type I and type II errors, significance levels, critical values, test statistics such as z and t, and the decision to reject or fail to reject the null hypothesis.
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
This chapter discusses chi-square tests and nonparametric tests. It covers performing chi-square tests to compare two or more proportions, test independence between categorical variables using contingency tables, and introduce nonparametric tests including the Wilcoxon rank sum test and Kruskal-Wallis test. Examples are provided to demonstrate chi-square tests of equality of proportions, independence, and expected versus observed frequencies in contingency tables.
Course Project, Part IIntroduction(REMOVE THIS LINE PRIOR CruzIbarra161
Course Project, Part I
Introduction
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Summarize what you have learned about confidence intervals. Discuss why it would be important to know the population mean of the data used for this term. Is this an important health measure?)
Sample Data
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: List ALL of the sample data in the table below.)
Directions:
1. Use the table above to create an 80%, 95%, and 99% confidence interval.
2. Choose another confidence level (besides 80%, 95% or 99%) to create another confidence interval.
3. Provide a sentence for each confidence interval created above which explains what the confidence interval means in context of topic of your project.
Computations
(Round all values to TWO decimal places)
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Calculate each of the following.)
Sample Mean =
Sample Standard Deviation =
80% Confidence Interval:
80% Confidence Interval Margin of Error:
Sentence:
95% Confidence Interval:
95% Confidence Interval Margin of Error:
Sentence:
99% Confidence Interval:
99% Confidence Interval Margin of Error:
Sentence:
______% Confidence Interval:
______% Confidence Interval Margin of Error:
Sentence
Problem Analysis
(REMOVE THESE LINES PRIOR TO SUBMITTING REPORT: Write a half-page reflection. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?)
Course Project, Part II
Preliminary Calculations
Round Preliminary Values to the nearest whole number.
Summary Table for:
Live Births
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Deaths
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Divorces
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Marriages
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Hypothesis Testing
With the information that you gather from the Summary Tables above, test the following (you can use excel when appropriate):
Hypothesis Test #1:
Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.
Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test.
Ho: μ ≥ ≤ =
Ha: μ < > ≠
Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test
Step 2: Determine the Rejection Region
Pick ONE multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.
a) ...
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each group
Decision Rule:
a. If the confidence interval (CI) overlap, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) do not include the null, then the decision must be to reject the H0.
7
2.Test Statistic
Calculate the test statistic (TS)
Obtain the critical value (CV) from the reference table
Decision Rule:
a. If the test statistic is in the FTR region, then the decision must be to fail to reject the H0.
b. If the test statistic is in the rejection region, then the decision must be to reject the H0.
FTR
CV
TS
Since the test statistic is in the rejection region, reject the H0
FTR
CV
Since the test statistic is in the fail to reject region, fail to reject the H0
TS
CV
CV
8
3. P-Value
Choose α
Calculate value of test statistic from your data
Calculate P- value from test statistic
Decision Rule:
a. If the p-value is less than the level of significance, α, then the decision m.
This chapter discusses hypothesis testing and its key concepts. It defines a hypothesis as a statement about a population parameter that is tested. The five steps of hypothesis testing are outlined as defining the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining a decision rule, and making a conclusion. The differences between one-tailed and two-tailed tests are explained. Examples are provided for conducting hypothesis tests on population means and proportions. The chapter also defines Type I and Type II errors and how to compute the probability of a Type II error.
This chapter discusses the fundamentals of hypothesis testing, including:
- The basic process involves stating a null hypothesis, collecting sample data, calculating a test statistic, and determining whether to reject or fail to reject the null hypothesis based on critical values.
- Type I and Type II errors can occur depending on whether the null hypothesis is true or false and the decision that is made. Researchers aim to control the level of Type I errors.
- 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 p-value approach compares the calculated p-value to the significance level to determine whether to reject the null hypothesis.
Similar to Fundamentals of Testing Hypothesis (20)
Konsep Balanced Score Card. Penilaian kinerja dilihat dari 4 perspektif yaitu perspektif keuangan, konsumen, learn and growth dan proses bisnis internal.
Dokumen tersebut membahas prospek industri taksi di Jakarta yang padat. Bakri mempertimbangkan untuk memasuki bisnis ini namun perlu menganalisis apakah dapat bersaing, bagaimana memulai usaha, kerja sama dengan investor dan mekanisme kerja sama dengan supir taksi.
Bakri berencana memasuki bisnis taksi di Jakarta. Analisis lingkungan eksternal menunjukkan prospek bisnis taksi masih baik meskipun persaingan ketat. Bakri perlu strategi yang tepat untuk bersaing di pasar yang padat.
Makalah Analisis PT Kereta API Indonesia . membahas analisis strategik dalam perusahaan kereta api, dimana dampak peraturan harga pesawat tidak ada penetapan batas bawah maka kereta api berdampak.
Makalah Analisis PT Kereta API Indonesia . membahas analisis strategik dalam perusahaan kereta api, dimana dampak peraturan harga pesawat tidak ada penetapan batas bawah maka kereta api berdampak.
Dmfi booklet indonesian. isi petisi nya yah jangan lupa klik www.dogmeatfreeindonesia.org
tidak sampai 1 menit isi petisi ini agar indonesia bebas dari daging anjing, anjing layak diperlakukan layak dan lebih baik.
tolong ya teman - teman
Dokumen tersebut membahas risiko kesehatan dan kesejahteraan hewan yang ditimbulkan oleh perdagangan daging anjing di Indonesia, termasuk penyebaran penyakit rabies, penderitaan hewan, dan kerentanan kelompok tertentu terhadap penyakit. Beberapa organisasi berkomitmen untuk meningkatkan kesadaran masyarakat dan mendorong pemerintah mengakhiri praktik ini.
BPR adalah merancang ulang radikal sistem bisnis untuk meningkatkan kinerja kritis seperti biaya, kualitas, layanan dan kecepatan. Faktor keberhasilan BPR meliputi visi, keterampilan, insentif, sumber daya, dan rencana aksi. Hasil yang diharapkan dari BPR adalah perbaikan proses hingga 100% dan pengurangan biaya secara drastis.
Makalah ini membahas tentang Business Process Reengineering (BPR), termasuk definisi, pihak yang terlibat, tahapan pelaksanaannya, dan faktor-faktor keberhasilannya. BPR merupakan perancangan ulang mendasar dan radikal sistem bisnis untuk meningkatkan kinerja perusahaan secara signifikan."
Balanced Scorecard (BSC) adalah sistem pengelolaan strategis yang menggabungkan ukuran-ukuran keuangan dan nonkeuangan untuk menyelaraskan strategi perusahaan. BSC memiliki empat perspektif yaitu keuangan, pelanggan, proses internal, dan pembelajaran & pertumbuhan. Langkah-langkah penyusunan BSC meliputi penetapan masalah, indikator kinerja utama, pengukuran KPI, dan pembuatan peta strategi.
Makalah ini membahas tentang Balanced Scorecard, yaitu sistem pengukuran kinerja yang mempertimbangkan empat perspektif yaitu keuangan, pelanggan, proses bisnis internal, dan pembelajaran dan pertumbuhan. Balanced Scorecard dikembangkan untuk mengurangi kelemahan pengukuran kinerja konvensional yang hanya berfokus pada aspek keuangan."
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
Dynamic policy enforcement is becoming an increasingly important topic in today’s world where data privacy and compliance is a top priority for companies, individuals, and regulators alike. In these slides, we discuss how LinkedIn implements a powerful dynamic policy enforcement engine, called ViewShift, and integrates it within its data lake. We show the query engine architecture and how catalog implementations can automatically route table resolutions to compliance-enforcing SQL views. Such views have a set of very interesting properties: (1) They are auto-generated from declarative data annotations. (2) They respect user-level consent and preferences (3) They are context-aware, encoding a different set of transformations for different use cases (4) They are portable; while the SQL logic is only implemented in one SQL dialect, it is accessible in all engines.
#SQL #Views #Privacy #Compliance #DataLake
Codeless Generative AI Pipelines
(GenAI with Milvus)
https://ml.dssconf.pl/user.html#!/lecture/DSSML24-041a/rate
Discover the potential of real-time streaming in the context of GenAI as we delve into the intricacies of Apache NiFi and its capabilities. Learn how this tool can significantly simplify the data engineering workflow for GenAI applications, allowing you to focus on the creative aspects rather than the technical complexities. I will guide you through practical examples and use cases, showing the impact of automation on prompt building. From data ingestion to transformation and delivery, witness how Apache NiFi streamlines the entire pipeline, ensuring a smooth and hassle-free experience.
Timothy Spann
https://www.youtube.com/@FLaNK-Stack
https://medium.com/@tspann
https://www.datainmotion.dev/
milvus, unstructured data, vector database, zilliz, cloud, vectors, python, deep learning, generative ai, genai, nifi, kafka, flink, streaming, iot, edge
4th Modern Marketing Reckoner by MMA Global India & Group M: 60+ experts on W...Social Samosa
The Modern Marketing Reckoner (MMR) is a comprehensive resource packed with POVs from 60+ industry leaders on how AI is transforming the 4 key pillars of marketing – product, place, price and promotions.
The Building Blocks of QuestDB, a Time Series Databasejavier ramirez
Talk Delivered at Valencia Codes Meetup 2024-06.
Traditionally, databases have treated timestamps just as another data type. However, when performing real-time analytics, timestamps should be first class citizens and we need rich time semantics to get the most out of our data. We also need to deal with ever growing datasets while keeping performant, which is as fun as it sounds.
It is no wonder time-series databases are now more popular than ever before. Join me in this session to learn about the internal architecture and building blocks of QuestDB, an open source time-series database designed for speed. We will also review a history of some of the changes we have gone over the past two years to deal with late and unordered data, non-blocking writes, read-replicas, or faster batch ingestion.
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...sameer shah
"Join us for STATATHON, a dynamic 2-day event dedicated to exploring statistical knowledge and its real-world applications. From theory to practice, participants engage in intensive learning sessions, workshops, and challenges, fostering a deeper understanding of statistical methodologies and their significance in various fields."
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...Aggregage
This webinar will explore cutting-edge, less familiar but powerful experimentation methodologies which address well-known limitations of standard A/B Testing. Designed for data and product leaders, this session aims to inspire the embrace of innovative approaches and provide insights into the frontiers of experimentation!