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.
The document discusses different types of two-sample hypothesis tests, including tests comparing two population means of independent samples, two population proportions, and paired or dependent samples. It provides examples and step-by-step explanations of how to conduct two-sample t-tests, z-tests, and tests of proportions. Key points covered include determining the appropriate test statistic based on sample size and characteristics, stating the null and alternative hypotheses, test criteria, and decisions rules.
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.
The document discusses different types of two-sample hypothesis tests, including tests comparing two population means of independent samples, two population proportions, and paired or dependent samples. It provides examples and step-by-step explanations of how to conduct two-sample t-tests, z-tests, and tests of proportions. Key points covered include determining the appropriate test statistic based on sample size and characteristics, stating the null and alternative hypotheses, test criteria, and decisions rules.
This document provides an overview of analysis of variance (ANOVA). It lists the goals as conducting hypothesis tests to determine if variances or means of populations are equal. It describes the characteristics of the F-distribution and how it is used to test hypotheses about equal variances or means. Examples are provided to demonstrate comparing two variances, comparing means of two or more groups, and constructing confidence intervals for differences in means. The key steps of ANOVA including organizing data in an ANOVA table and making conclusions based on the F-statistic are outlined.
This document outlines the steps for hypothesis testing, including:
1. Defining the null and alternative hypotheses (H0 and H1). H0 is presumed true while H1 has the burden of proof.
2. Conducting a 5-step hypothesis testing procedure: state hypotheses, select significance level, select test statistic, formulate decision rule, make decision and interpret.
3. Distinguishing between one-tailed and two-tailed tests. Keywords in the problem statement determine if it is left-tailed, right-tailed, or two-tailed.
4. Examples are provided for testing hypotheses about population means when the population standard deviation is known or unknown, and for testing hypotheses about
This document provides an overview of multiple linear regression analysis. It describes using multiple regression to model the relationship between a dependent variable and multiple independent variables. Key points covered include: setting up and interpreting a multiple regression equation; computing measures like the standard error, coefficient of determination, and adjusted coefficient of determination; conducting hypothesis tests on the regression coefficients and overall model; evaluating assumptions; and using residual analysis to validate the model. An example is presented using data on home heating costs to develop a multiple regression model relating costs to temperature, insulation, and furnace age.
This chapter discusses choosing appropriate statistical techniques for analyzing numerical and categorical data. For numerical variables, it identifies questions about describing characteristics, drawing conclusions about the mean/standard deviation, determining differences between groups, identifying influencing factors, predicting values, and determining stability over time. For each, it lists relevant techniques. For categorical variables, it addresses similar questions and outlines techniques like hypothesis testing, regression, and control charts. The goal is to match the right analysis to the data type and research purpose.
This document provides an overview of decision making techniques covered in Chapter 17. It begins by listing the learning objectives, which are to use payoff tables, decision trees, and criteria to evaluate alternative courses of action. It then outlines the steps in decision making, which include listing alternatives and uncertain events, determining payoffs, and adopting evaluation criteria. Several decision making criteria are introduced, including maximax, maximin, expected monetary value, expected opportunity loss, value of perfect information, and return-to-risk ratio. Payoff tables and decision trees are presented as methods for displaying decision problems. The chapter concludes by discussing how sample information can be used to revise old probabilities when making decisions.
This document provides an overview of time-series forecasting and index numbers. It discusses different time-series forecasting models including moving averages, exponential smoothing, linear trend, quadratic trend, and exponential trend models. It also covers identifying trend, seasonal, and irregular components in a time series. Smoothing methods like moving averages and exponential smoothing are presented as ways to identify trends in data. The document concludes by discussing linear, nonlinear, and exponential trend forecasting models for generating forecasts from time-series data.
This document provides an overview of multiple regression analysis. It introduces the concept of using multiple independent variables (X1, X2, etc.) to predict a dependent variable (Y) through a regression equation. It presents examples using Excel and Minitab to estimate the regression coefficients and other measures from sample data. Key outputs include the regression equation, R-squared (proportion of variation in Y explained by the X's), adjusted R-squared (penalized for additional variables), and an F-test to determine if the overall regression model is statistically significant.
This document provides an overview of simple linear regression analysis. It defines key concepts such as the regression line, slope, intercept, and correlation coefficient. It also explains how to evaluate the fit of a regression model using the coefficient of determination (R2), which measures the proportion of variance in the dependent variable that is explained by the independent variable. The document includes an example using house price and square footage data to demonstrate how to apply simple linear regression and interpret the results.
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 analysis of variance (ANOVA) techniques. It covers one-way and two-way ANOVA for comparing the means of three or more groups or populations. The chapter explains how to partition total variation into between-group and within-group components using sum of squares calculations. It also describes how to conduct the F-test and make inferences about differences in population means using ANOVA tables and significance tests. Multiple comparison procedures for identifying specific mean differences are also introduced.
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.
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 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 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 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 basic probability concepts covered in Chapter 4 of Basic Business Statistics, 11th Edition. It introduces key probability terms like simple events, joint events, sample space, and contingency tables for visualizing events. It covers how to calculate probabilities of events both with and without conditional dependencies. Formulas are provided for computing joint, marginal, and conditional probabilities using contingency tables. The chapter also explains Bayes' Theorem for revising probabilities based on new information. An example demonstrates how to apply Bayes' Theorem to calculate the probability of a successful oil well given a positive test result.
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.
This document discusses various methods for organizing and presenting categorical and numerical data using tables, charts, and graphs. It covers summarizing categorical data using summary tables, bar charts, pie charts, and Pareto diagrams. For numerical data, it discusses organizing data using ordered arrays, stem-and-leaf displays, frequency distributions, histograms, frequency polygons, ogives, contingency tables, side-by-side bar charts, and scatter plots. The goal is to effectively communicate patterns and relationships in the data.
This chapter introduces basic concepts in business statistics including how statistics are used in business, types of data and their sources, and popular software programs like Microsoft Excel and Minitab. It discusses descriptive versus inferential statistics and reviews key terminology such as population, sample, parameters, and statistics. The chapter also covers different types of variables, levels of measurement, and considerations for properly using statistical software programs.
21. МАКРО ЭДИЙН ЗАСГИЙН ҮЗҮҮЛЭЛТ – Аж үйлдвэр
Аж үйлдвэрийн салбарын нийт үйлдвэрлэл,
2005 оны зэрэгцүүлэх үнээр, тэрбум төг
Аж үйлдвэрийн салбар 2011 2012 2013
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