北美学分课程项目
MATH 110: Introduction to Statistics

MATH 110: Introduction to Statistics

价格
4599.00
课程详情

课程描述

对数理统计作为决策过程中使用的工具的一般介绍。该课程旨在通过使用频率分布、集中趋势测量、分散测量、概率分布、随机抽样、区间估计、假设检验、涉及的比较来帮助学生理解描述性和推理性统计应用中的汇总数据均值和回归分析。

学分:3

先决条件:要求精通代数(高中代数 2 或大学同等水平)

课程主题

模块 1:数据和统计简介。本模块讨论为什么统计很重要,以及统计分析的用途。学生将了解可能用于统计分析的不同类型的数据。涵盖的主题包括:定量和定性数据、实验和观察研究、数据错误、离群值、描述性统计、直方图、人口和样本。

模块 2:介绍使用表格、图形和数值方法进行的描述性统计。该模块考虑描述和表示数据的方法。涵盖的主题包括:频率分布、相对频率、图表(柱形图、条形图和饼图)、交叉表、散点图、集中趋势测量、百分位数、四分位数、离差测量、Z 分数、钟形曲线和样本协方差.

模块 3:概率概述。该模块考虑实验和事件发生的可能性。教导学生使用多种技术计算概率。涵盖的主题包括:概率分布、样本空间、计数技术、排列、组合、互补、并集、交集、互斥事件、条件概率和贝叶斯定理。

模块 4:概率分布简介。学生将了解标准正态概率分布,以及数据如何相对于均值分布。涵盖的主题包括:随机变量(离散和连续)、期望值、二项式概率分布、正态分布和标准正态表。

模块 5:抽样和抽样分布概述。本模块解释了在使用样本而不是整个总体时如何计算描述性统计数据。涵盖的主题包括:统计推断、简单随机样本、样本均值、样本比例、中心极限定理、样本误差和样本大小。

模块 6:区间估计简介。在本模块中,学生将学习如何取样、求出其均值并使用此信息来估计总体均值。学生将能够构建总体均值的置信区间。涵盖的主题包括:置信区间、置信水平、均值和比例。

模块 7:假设检验简介。在本模块中,学生将被引导完成假设检验的过程。学生将学习对人口的某些特征做出假设,然后检验该假设是否正确。涵盖的主题包括:无效假设、备择假设、单尾和双尾检验、I 类和 2 类错误以及显着性水平。

模块 8:介绍涉及均值和比例的比较。在本模块中,学生将研究区间估计和假设检验,以了解两个总体均值之间的差异以及两个总体比例之间的差异。涵盖的主题包括:相关样本、独立样本、涉及均值差异的假设检验以及相关样本的假设检验。

模块 9:回归分析简介。学生将学习如何计算一组数据的线性相关系数,以揭示两个变量的相关程度。学生还将学习如何找到最接近这些变量之间关系的**拟合线。涵盖的主题包括:线性相关系数、正相关、负相关、临界值相关系数和线性回归

模块 10:概述之前模块中未涵盖的各种测试。学生将学习拟合优度检验、独立性检验和方差分析。涵盖的主题包括:卡方分布、F 分布、多项式实验、预期计数、拟合优度检验和独立性检验。

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Course Description

A general introduction to mathematical statistics as a tool used in the decision-making process. The course is designed to help students develop an understanding of summarized data in both descriptive and inferential statistical applications through the use of frequency distributions, measures of central tendency, measures of dispersion, probability distributions, random sampling, interval estimation, hypothesis testing, comparisons involving means, and regression analysis.

CREDITS: 3

Prerequisites: Algebra proficiency required (high-school algebra 2 or a college equivalent)

Course Topics

Module 1: An introduction to data and statistics. This module discusses why statistics are important, and where statistical analysis is used. Students will learn about different types of data that might be used in statistical analysis. Topics covered include: Quantitative and Qualitative Data, Experimental and Observational Studies, Data Errors, Outliers, Descriptive Statistics, Histograms, Populations, and Samples.

Module 2: An introduction to descriptive statistics using tabular, graphical and numerical methods. This module considers ways to describe and represent data. Topics covered include: Frequency Distributions, Relative Frequencies, Charts (Column, Bar, and Pie), Cross-Tabulation, Scatter Diagrams, Measures of Central Tendency, Percentiles, Quartiles, Measures of Dispersion, Z-scores, Bell Curves, and Sample Covariance.

Module 3: An overview of probability. This module considers experiments and the likelihood that an event will occur. Students are taught to calculate probabilities using multiple techniques. Topics covered include: Probability Distributions, Sample Space, Counting Techniques, Permutations, Combinations, Complements, Union, Intersection, Mutually Exclusive Events, Conditional Probabilities, and Bayes’ Theorem.

Module 4: An introduction to probability distributions. Students will learn about the standard normal probability distribution, and how the data is distributed with respect to the mean. Topics covered include: Random Variables (Discrete and Continuous), Expected Values, Binomial Probability Distributions, Normal Distributions, and The Standard Normal Table.

Module 5: An overview of sampling and sampling distributions. This module explains how to calculate descriptive statistics when working with a sample instead of the entire population. Topics covered include: Statistical Inference, Simple Random Samples, Sample Mean, Sample Proportions, The Central Limit Theorem, Sample Error, and Sample Size.

Module 6: An introduction to interval estimation. In this module students will learn how to take a sample, find its mean, and use this information to estimate the population mean. Students will be able to construct confidence intervals for the population mean. Topics covered include: Confidence Intervals, Confidence Levels, Means, and Proportions.

Module 7: An introduction to hypothesis testing. In this module students will be guided through the process of hypothesis testing. Students will learn to make assumptions about a certain characteristic of the population and then test to see if the hypothesis is true. Topics covered include: Null Hypothesis, Alternate Hypothesis, One-Tailed and Two-Tailed Tests, Type I and Type 2 errors, and Level of Significance.

Module 8: An introduction to comparisons involving means and proportions. In this module students will study interval estimation and hypothesis testing for differences between two population means as well as for differences between two population proportions. Topics covered include: Dependent Samples, Independent Samples, Hypothesis Testing Involving Differences between Means, and Hypothesis Testing for Dependent Samples.

Module 9: An introduction to regression analysis. Students will learn how to calculate the linear correlation coefficient for a set of data to reveal how well two variables are correlated. Students will also learn how to find the best fit line that approximates the relationship between these variables. Topics covered include: Linear Correlation Coefficients, Positive Correlations, Negative Correlations, Critical Values Correlation Coefficient, and Linear Regression

Module 10: An overview of various tests that were not covered in previous modules. Students will learn about goodness of fit tests, tests for independence, and analysis of variance. Topics covered include: Chi-Square Distributions, F Distributions, Multinomial Experiments, Expected Counts, Goodness of Fit Tests, and Tests for Independence.