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原创 美国高中学分课 36周 AP Statistics

原创:Sagittar Academy 公众号 英语学分课适合就读国际学校、国际部、国际班,想申请美国大学、加拿大大学、英国大学的学生

原创:Sagittar Academy 公众号 英语学分课

适合就读国际学校、国际部、国际班,想申请美国大学、加拿大大学、英国大学的学生

1

课程简介

AP®Statistics 相当于大学一学期的非以计算为基础的统计学入门课程。本课程的严谨和节奏与许多学院和大学提供的非基于计算的统计课程一致,并将帮助学生准备大学预修考试。成功完成考试后,学生可以获得大学学分,并为额外的高级课程做好准备。

AP统计向学生介绍主要概念,包括收集、分析数据和从数据中得出结论。本课程分为四个主要主题:(1)数据探索,(2)抽样与实验,(3)预测模式,(4)统计推断。本课程允许学生通过讨论、数据收集活动、调查和进行统计研究的期末项目来获得概念上的理解。为了准备考试,学生将完成每周AP®练习小测验和单元考试,这将符合AP®考试的限制。

这门AP®课程有一个必须的暑期作业。学生必须在课程开始前完成他们的暑期作业,并在第一周结束前提交作业。9月1日或之后注册的学生将获得延期,在第三周结束前完成暑期作业。暑期作业的目的是在适用的情况下,复习与课程的先决知识相关的关键内容,并让学生更好地理解与内容相关的严谨性。

2

课程目标

  • Describe patterns and departures from patterns
  • Plan and conduct a study
  • Explore random phenomena using probability and simulation
  • Estimate population parameters and test hypotheses.

3

课程安排及要求

  • 秋季2020年9月2日开始,换课、退课限9月8日前
  • 平均每周学习时间10-12小时
  • 每周完成阅读要求,参与课堂讨论,提交作业
  • 学生学过代数2,自备图形计算器,推荐型号 TI83 或 TI84

4

课程优势

学分被以下认证机构认可

CollegeBoard

NACC

Cognia (AdvancED)

Middle States Commission on Secondary Schools

如学生表现好,申请海外大学可以有老师推荐信

课程师资

86%的教师拥有7年以上一线教学经验,81%的教师拥有硕士以上学位,每位教师都修完在线教学方法课程( Online Teaching Methodologies )。OTM是一门研究生水平的在线课程,侧重于在在线课堂中建立社区、促进有意义的讨论和提供有洞察力的反馈的教学策略。

Weekly Pace灵活的课程

本课程结合了传统的教师主导的、小班教学的优点,同时保持了进度灵活性。每学期的课程遵循Weekly Paced 每周进度的模式,学生选择自己最适合的时间学习,但必须每周完成指定工作量,与小组同学和老师保持沟通。

5

招生要求

  • 招收 10,11,12年级学生
  • TOEFL (90+)
  • MAP测试成绩单
  • 国际学校成绩单
  • 或其他英语能力证明
  • 电话 15601221714 微信公众号 英语学分课

6

课程大纲

Week 1: Welcome to AP® Statistics

Essential Question: How do we get started?

Objectives:

Familiarize yourself with the rules and policies of the course

Complete a survey about yourself and your school

Meet your classmates and get comfortable navigating in the course

Understand what is expected of you throughout this course

Work collaboratively with your peers to build a “social contract” for a productive community of learners.

Week 2: Exploring Categorical Data

Essential Question: Does data always reveal the truth?

Objectives:

Identify the two branches of statistics and define individuals and variables of data sets

Identify the difference between categorical and quantitative data

Conduct a lab to identify the distribution of categorical data

Identify and create graphs of categorical data: pie charts, bar graphs

Interpret two-way tables and their conditional distributions

Week 3: Exploring Quantitative Data Graphically

Essential Question: Does data always reveal the truth?

Objectives:

Identify dotplots, stemplots and histograms and their features

Construct dotplots, stemplots and histograms

Interpret the shape, center, spread and any unusual features of a distribution

Determine the shape, center, spread and any unusually features from graphs of quantitative data

Week 4: Exploring Quantitative Data Numerically

Essential Question: Does data always reveal the truth?

Objectives:

Identify and interpret the measures of center: mean, median and mode

Identify quartiles and the five-number summary

Identify and interpret the measures of spread: range, IQR and standard deviation

Determine if any outliers exist in a data set

Construct and interpret boxplots

Interpret numerical summaries to compare quantitative data distributions

Week 5: Modeling with the Normal Distribution

Essential Question: What is normal?

Objectives:

Identify and interpret measures of position: percentiles and z-scores

Identify the effect of adding, subtracting, multiplying or dividing by a constant on the shape, center and spread of a data distribution

Identify the normal distribution and its characteristics

Use the 68-95-99.7 Rule to estimate the proportion of observations of a normal distribution

Use the standard normal distribution to determine the proportion of values in a particular interval

Use technology to interpret normal distributions

Week 6: Scatterplots and Correlation

Essential Question: How can we determine if there is a relationship between two quantitative variables?

Objectives:

Identify and interpret scatterplots

Identify and interpret the strength and direction of a scatterplot

Determine the difference between association and correlation

Interpret the correlation coefficient of bivariate data

Week 7: Linear Regression

Essential Question: How can we model the linear relationship between two quantitative variables?

Objectives:

Identify if a scatterplot takes on a linear form

Identify and interpret the least-squares regression line

Find and describe residuals

Construct and interpret residual plots

Identify and interpret the coefficient of determination

Explain why association does not imply causation

Interpret the effect of unusual features and outliers

Week 8: Transforming Data to Achieve Linearity

Essential Question: How can we achieve linear data?

Objectives:

Transform data with powers

Transform data with roots

Transform data with logarithms

Week 9: Sampling Methods

Essential Question: How can we gather data?

Objectives:

Identify the difference between a population and a sample

Distinguish between good and bad sampling methods

Identify advantages and disadvantages of various sampling methods

Apply a table of random digits

Identify possible bias in sampling methods

Week 10: Experimental Design

Essential Question: How can we gather data?

Objectives:

Identify the difference between an observational study and an experiment

Identify a lurking variable and their affect on data

Explain the importance of random assignment

Identify the effect of a placebo

Identify experimental design

Week 11: Probability and Simulation

Essential Question: Is what should happen what will happen?

Objectives:

Interpret the meaning of probability

Relate probability to a relative frequency

Use simulation to model chance behavior

Week 12: Probability Rules

Essential Question: Is what should happen what will happen?

Objectives:

Describe the probability distribution of an experiment

Identify and apply the basic probability rules: complement rule, and addition rule for mutually exclusive events

Apply Venn diagrams to model an experiment involving two events

Identify and apply the general addition rule

Week 13: Independence and Conditional Probabilities

Essential Question: Is what should happen what will happen?

Objectives:

Identify and apply tree diagrams to determine the chance of compound events

Identify and apply the multiplication rule

Identify events as independent or dependent

Find the probability of independent events

Find the conditional probabilities of dependent events

Week 14: Semester Review

Essential Question: What have we learned this semester?

Objectives:

Discuss the importance of statistics

Review important vocabulary covered this semester

Prepare for your midterm exam

Week 15: Semester Exam and AP® Review

Essential Question: What have we learned this semester?

Objectives:

Share study tips and ask questions about the AP® Exam

Prepare for your midterm exam

Complete AP® practice quizzes

Week 16: Random Variables

Essential Questions: What is a random variable? How do random variables relate to probability?

Objectives:

Identify discrete and continuous random variables

Calculate and interpret the mean and standard deviation of a random variable

Interpret effects of transforming a random variable by adding, subtracting, multiplying or dividing by a constant

Identify independent random variables

Find the mean and standard deviation of the sum and difference of random variables

Week 17: Binomial and Geometric Distributions

Essential Question: What is a success?

Objectives:

Determine the conditions of a binomial random variable

Calculate and interpret the mean and standard deviation of a binomial random variable

Calculate and interpret probabilities involving binomial and geometric distributions

Determine the conditions for the Normal approximation to the binomial distribution

Apply the Normal approximation to estimate probabilities for a binomial setting

Week 18: Sampling Distributions and Sample Proportions

Essential Question: How is a sample used to describe a population?

Objectives:

Identify the difference between a statistic and a parameter

Determine whether a statistic is an unbiased estimator of a population

Interpret the relationship between sample size and the variability of an estimator

Find the mean and standard deviation of the sampling distribution of a sample proportion

Check and apply the 10% and Normal conditions to approximate probabilities of p-hat

Week 19: Sample Means and the Central Limit Theorem

Essential Question: How is a sample used to describe a population?

Objectives:

Find the mean and standard deviation of the sampling distribution of a sample mean

Calculate probabilities involving a sample mean when the population distribution is Normal

Interpret the shape of the sampling distribution related to the shape of the population distribution

Interpret and apply the Central Limit Theorem

Week 20: Confidence Intervals

Essential Question: How is statistical inference used to draw conclusions from data?

Objectives:

Identify a confidence interval

Interpret confidence intervals within context

Identify and interpret the three inference conditions: random, normal and independent

Week 21: Estimating a Population Proportion

Essential Question: How is statistical inference used to draw conclusions from data?

Objectives:

Construct and interpret a confidence interval for a population proportion

Determine critical values

Interpret confidence intervals within context

Determine the required sample size to obtain a level C confidence interval with a specific margin of error

Interpret the margin of error

Week 22: Estimating a Population Mean

Essential Question: How is statistical inference used to draw conclusions from data?

Objectives:

Construct and interpret a confidence interval for a population mean

Determine the required sample size to obtain a level C confidence interval with a specific margin of error

Determine sample statistics from a confidence interval

Week 23: Significance Tests – Introduction

Essential Question: How can we test a claim?

Objectives:

State the null and alternative hypotheses for a significance test about a population parameter

Interpret a P-value in context

Determine if results of a study are statistically significant and make appropriate conclusions

Interpret a Type I and Type II error in context

Week 24: Significance Tests – Population Proportion

Essential Question: How can we test a claim?

Objectives:

State and check the random, 10% and large counts conditions for performing a significance test

Perform a significance test about a population proportion

Interpret the power of a test

Describe the relationship among the probability of Type I error, the probability of Type II error and the power of a test

Week 25: Significance Tests – Population Mean

Essential Questions: How can we test a claim?

Objectives:

State and check the random, 10% and large counts conditions for performing a significance test

Perform a significance test about a population mean

Use a confidence interval to draw a conclusion for a two-sided test about a population parameter

Perform a significance test about a mean difference using paired data

Week 26: Comparing Two Proportions

Essential Question: How can we compare two quantities?

Objectives:

Describe the shape, center and spread of sampling distribution of a difference of proportions

Determine if the conditions are met for inference of difference of proportions

Construct and interpret a confidence interval to compare two proportions

Perform a significance test to compare two proportions

Week 27: Comparing Two Means

Essential Question: How can we compare two quantities?

Objectives:

Describe the shape, center and spread of sampling distribution of a difference of means

Determine if the conditions are met for inference of difference of means

Construct and interpret a confidence interval to compare two means

Perform a significance test to compare two means

Determine when to use two-sample t procedures versus paired t procedures

Week 28: Chi-Square Goodness-of-Fit Tests

Essential Question: How do we apply chi-square tests?

Objectives:

Identify appropriate hypotheses and compute expected counts for a chi-square test for goodness of fit

Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test for goodness of fit

Perform a chi-square test for goodness of fit

Analyze the results of a chi-square test when the results are statistically significant

Review the project introduction

Week 29: Inference for Relationships

Essential Question: How do we apply inference?

Objectives:

Compare conditional distributions for data in a two-way table

Identify appropriate hypotheses and compute expected counts for a chi-square test based on data in a two-way table

Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test based on data in a two-way table

Perform a chi-square test for homogeneity

Perform a chi-square test for independence

Choose the appropriate chi-square test

Create a project proposal

Week 30: Inference for Linear Regression

Essential Question: How do we apply inference?

Objectives:

Identify the conditions for performing inference about the slope of the population regression line

Identify and interpret values in context as well as from computer output

Construct and interpret a confidence interval for the slope of the population regression line

Perform a significance test about the slope of the population regression line

Collect data for project

Week 31: AP® Review and Preparing for the Exam

Essential Question: How do we prepare for the AP® Exam?

Objectives:

Review information in regards to the AP® Exam

Take a complete practice AP® Exam

Analyze collected data for project

Week 32: AP® Review and Final Project

Essential Question: How do we prepare for the AP® Exam?

Objectives:

Review multiple choice questions on the complete practice exam

Review the free response questions on the complete practice exam

Perform inference for project

Gather conclusions for project

Week 33: Project Presentations and Wrapping Up AP® Statistics

Essential Question: What have we learned in the course?

Objectives:

Investigate careers that apply statistics

Present your project presentation

Complete your final reflection

Complete end of course surveys

eBook: The Practice of Statistics for AP

ISBN: Print: ISBN-13 9781464108730

Pub: W.H. Freeman

Author (Last + First name): Starnes, Daren S.

Edition/Date: Fifth Edition, 2015

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