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WCHS AP Statistics Pacing Guide (S-2015)

1/12/15

Chapter 1 - Exploring Data

Day Topics Objectives Homework

1

Hyena Lab Chap 1 Introduction

Identify the individuals and variables in a set of data

Classify variables as categorical or quantitative

Read pp 1-8 1, 3, 5, 7, 8

2

1.1 Bar graphs, pie charts, good & bad graphs; two-way tables, marginal distributions, relationships between categorical variables, conditional distributions, organizing a statistical problem

Make a bar graph of the distribution of a categorical variable

Recognize when a pie chart can and cannot be used

Identify what makes some graphs deceptive

From a two-way table, answer questions involving marginal and conditional distributions

Describe the relationship between two categorical variables by computing appropriate conditional distributions

Construct bar graphs to display the relationship between two categorical variables

Read pp 8-26 11-25 odd, 27-32

3

1.2 Dotplots, describing shape, comparing distributions, stemplots, histograms, using histograms wisely

Make a dotplot or stemplot

Describe the overall pattern (shape, center, spread) of a distribution and identify major departures from the pattern (like outliers)

Identify the shape of a distribution from a dotplot, stemplot, or histogram as roughly symmetric or skewed, identify the number of modes

Interpret histograms

Read pp 27-41 37-45 odd,49, 52, 54, 59, 69-74

4

1.3 Measuring center: mean & median, comparing mean & median; Measuring spread: IQR; identifying outliers; 5-number summary and boxplots; measuring spread: standard deviation, choosing measures of center and spread

Calculate and interpret measures of center (mean & median)

Calculate and interpret measures of spread (IQR)

Identify outliers (1.5 x IQR Rule)

Make a boxplot

Calculate & interpret measures of spread (standard deviation)

Select appropriate measures of center and spread

Use appropriate graphs and numerical summaries to compare distributions of quantitative variables

Read pp 50-69 79-91 odd, 103, 105, 107-110

5.1

Chapter Review Read NTA pp 11-17 Special Problem 1; Portfolio 1.1, 1.2


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Chapter 2 - Modeling Distributions of Data


5.2

2.1A Intro, measuring position: percentiles, cumulative relative frequency graphs, measuring position: z-scores

Use percentiles to locate individual values within distribution of data

Read pp 84-91 5-15 odd

6

2.1B Transforming data, density curves 2.2A Normal Distributions, 68-95-99.7 Rule, Standard Normal distribution

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

Approximately locate the median (equal areas point) and the mean (balance point) on a density curve

Use the 68-95-99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points 1, 2, and 3 standard deviations on either side of the mean

Use the standard Normal distribution to calculate the proportion of values in a specified interval

Use the standard Normal distribution to determine a z-score from a percentile

Read pp 92-104 19, 21, 23, 27, 33-38 Read pp 110-119 41-51 odd

7

2.2B Normal distribution calculations; assessing normality

Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile

Use a graphing calculator to do the same

Make an appropriate graph to determine if a distribution is bell-shaped

Read 119-130 53-59 odd, 63a,b, 68-74

8

Chapter Review Read NTA pp 19-25 Portfolio 2.1-2.5

9

Chapter 1/2 Exam Special Problem 2


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Chapter 3 – Describing Relationships


10

3.1 Intro; explanatory & response variables; displaying relationships: scatterplots; interpreting scatter plots; measuring linear association: correlation; facts about correlation

Describe why it is important to investigate relationships between variables

Identify explanatory and response variables in situations where one variable helps to explain or influences the other

Make a scatterplot to display the relationship between two quantitative variables

Describe the direction, form, and strength of the overall pattern of a scatterplot

Know the basic properties of correlation

Calculate and interpret correlation

Explain how the correlation r is influenced by extreme observations

Read pp 142-156 1, 5, 7, 11, 13, 14-18, 21, 26

11

3.2A Least-squares regression; interpreting regression line; prediction; residuals; calculating the equation of the least-squares regression line

Interpret the slope and y-intercept of a least-squares regression line

Use the least-squares regression line to predict a y for a given x

Explain the dangers of extrapolation

Calculate and interpret residuals

Explain the concept of least squares

Use technology to find a least-squares regression line

Find the slope and intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation

Read pp 164-174 27-32, 35-47 odd, 53

12

3.2B How well the line fits the data: residual plots; how well the line fits the data: the role of r2 in regression; interpreting computer output; correlation and regression wisdom

Construct and interpret residual plots to assess if a linear model is appropriate

Use the standard deviation of the residuals to assess how well the line fits the data

Use r2 to assess how well the line fits the data

Identify the equation of a least-squares regression line from computer output; Explain why association does not imply causation

Recognize how the slope, y intercept, standard deviation of the residuals, and r2 are influenced by extreme observations

Read 174-190 55-59 odd, 63, 65, 69, 71-78

13.1

Chapter Review Read NTA pp 27-33 Special Problem 3; Portfolio 3.1-3.6


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Chapter 4 – Designing Studies


14

4.1A Intro; Sampling and surveys; how to sample badly, how to sample well; random samples; other sampling methods

Identify the population and sample in a sample survey

Identify voluntary response samples and convenience samples; explain how these bad sampling methods can lead to bias

Describe how to use Table D to select a simple random sample (SRS)

Distinguish a simple random sample from a stratified or cluster sample; give advantages and disadvantages of each sampling method

Read pp 205-219 1-11 odd, 17-25 odd,

15

4.1B Inference for sampling; sample surveys: what can go wrong? 4.2A Observational studies vs. experiments; the language of experiments; how to experiment badly

Explain how undercoverage, nonresponse, and question wording can lead to bias in a sample survey

Distinguish between an observational study and an experiment

Explain how a lurking variable in an observational study can lead to confounding

Identify the experimental units or subjects, explanatory variables (factors), treatments, and response variables in an experiment

Read pp 220-225 27, 28, 29-35 odd Read pp 231-236 37-42, 45-53 odd

16

4.2 B How to experiment well; three principles of experimental design; experiments: what can go wrong; inference for experiments

Describe a completely randomized design for an experiment

Explain why random assignment is an important design principle

Describe how to avoid the placebo effect in an experiment

Explain the meaning and the purpose of blinding in an experiment

Explain in context what “statistically significant” means

Read pp 236-246 57, 63-75 odd

17

4.2C Blocking; matched pairs design

Distinguish between a completely randomized design and a randomized block design

Know when a matched pairs experimental design is appropriate and how to implement such a design

Read pp 246- 252 77, 79, 81, 85


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Chapter 4 – Designing Studies (cont)


18

4.3 Scope of inference; the challenges of establishing causation Class experiments

Determine the scope of inference for a statistical study

Read pp 261-265 91-98, 103, 105, 107, 108

19

Chapter Review Read NTA 35-41 Portfolio 4.1-4.7

20



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Chapter 5 – Probability


21

5.1 Intro; the idea of probability; myths about randomness; simulation

Interpret probability as a long-run relative frequency

Use simulation to model chance behavior

Read pp 282- 293 1, 3, 7, 9, 11, 15, 17, 23, 25, 37, 38

22

5.2 Probability models; basic rules of probability; two-way tables and probability; Venn diagrams and probability

Describe a probability model for a chance process

Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events

Use a Venn diagram to model a chance process involving two events

Use the general addition rule to calculate P(A|B)

Read 299-308 27, 29, 31, 32-36, 43-55 odd

23

5.3 What is conditional probability?; conditional probability and independence; tree diagrams and the general multiplication rule; independence: a special multiplication rule; calculating conditional probabilities

When appropriate, use a tree diagram to describe chance behavior

Use the general multiplication rule to solve probability questions

Determine whether two events are independent

Find the probability that an event occurs using a two-way table

When appropriate, use the multiplication rule for independent events to compute probabilities

Compute conditional probabilities

Read pp 312-328 57-60, 63-69 odd, 73, 77, 83, 85, 87, 91-99 odd

24

Chapter Review Read NTA pp 43-45 Special Problem 5 Portfolio 5.1-5.8


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Chapter 6 – Random Variables


25

6.1 Intro; discrete random variables; mean (expected value) of a discrete random variable; standard deviation (and variance) of a discrete random variable; continuous random variables

Use a probability distribution to answer questions about possible values of a random variable

Calculate the mean of a discrete random variable

Interpret the mean of a random variable

Calculate the standard deviation of a discrete random variable

Interpret the standard deviation of a random variable

Read pp 340-352 1, 5, 7, 9, 13, 14, 18, 19, 23, 25

26

6.2 Linear transformations; combining random variables; combining Normal random variables

Describe the effects of transforming a random variable by adding or subtracting a constant and multiplying or dividing by a constant

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

Determine whether two random variables are independent

Find the probabilities involving the sum or difference of independent Normal random variables

Read pp 358-377 27-30, 37, 39-41, 43, 45, 49, 51, 57-59, 63

27

6.3 Binomial settings and binomial random variables; binomial probabilities; mean and standard deviation of a binomial distribution; binomial distributions in statistical sampling; geometric random variables

Determine whether the conditions for binomial random variable are met

Compute and interpret probabilities involving binomial distributions

Calculate the mean and standard deviation of a binomial random variable; interpret the results in context

Find probabilities involving geometric random variables

Read pp 382-403 61, 65, 66, 69-89 odd, 101, 103

28

Chapter Review Read NTA pp 47-53 Portfolio 6.1-6.13

29


30

Cumulative Review

31

6-Week Exam


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Chapter 7 – Sampling Distributions and the Central Limit Theorem


32

7.1 Intro; German tank problem; parameters and statistics; sampling variability; describing sampling distributions

Distinguish between a parameter and a statistic

Understand the definition of a sampling distribution

Determine whether a statistic is an unbiased estimator of a population parameter

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

Read Sec 7.1 1-13 odd, 17-20

33

7.2 The sampling distribution of �̂�; using the Normal approximation for �̂�

Find the mean and standard deviation of the sampling distribution of a sample proportion �̂� for an SRS of size n from a population having p successes

Check whether the 10% and Normal conditions are met in a given setting

Use Normal approximation to calculate probabilities involving �̂�

Use the sampling distribution to evaluate a claim about a population proportion

Read Sec 7.2 21-24, 27, 29, 33, 35, 37, 41

34

7.3 The sampling distribution of �̅�; mean and standard deviation; sampling from a Normal distribution; the Central Limit Theorem

Find the mean and standard deviation of the sampling distribution of a sample mean �̅� from an SRS of size n

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

Explain how the shape of the sampling distribution of �̅� is related to the shape of the population distribution

Use the CLT to help find probabilities involving a sample mean �̅�

Read Sec 7.3 43-46, 49-65 odd, 66-68

35

Chapter Review

Read NTA pp 55-58 Special Problem 7 Portfolio 7.1-7.9


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Chapter 8 – Estimating with Confidence


36

8.1 The idea of a confidence interval; interpreting confidence levels and confidence intervals; constructing a confidence interval; using confidence intervals wisely

Interpret a confidence level

Interpret a confidence interval in context

Understand that a confidence interval gives a range of plausible values for a parameter

Understand why each of the three inference conditions – Random, Normal, and Independent – is important

Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval

Read Sec 8.1 5-13 odd, 17, 19-24

37

8.2 Conditions for estimating p; constructing a confidence interval for p; putting it all together: the 4-step process; choosing the sample size

Construct and interpret a confidence interval for a population proportion

Determine critical values for calculating a confidence interval using a table or your calculator

Carry out the steps in constructing a confidence interval for a population proportion; check conditions; perform calculations; interpret results in context

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

Understand how the margin of error of a confidence interval changes with the sample size and level of confidence C


Read Sec 8.2 27, 31-37 odd, 41, 43, 47

38

8.3 The one sample z-interval for a population mean; the t-distributions; constructing a confidence interval for

; using t procedures wisely

Construct and interpret a confidence interval for a population mean

Determine the sample size required to obtain a level C confidence interval for a population mean with a specified margin of error

Carry out the steps in constructing a confidence interval for a population mean; check conditions; perform calculations; interpret results in context


Read Sec 8.3 49-52, 55, 57, 59, 63, 65, 67, 71, 73, 75-78


1/12/15


39

Chapter Review

Determine sample statistics from a confidence interval

Read NTA pp 559-564 Portfolio 8.1-8.8

40 Chapter 7/8 Exam Special Problem 8


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Chapter 9 – Testing a Claim


41

9.1 The reasoning of significance tests; stating hypotheses; interpreting p-values; statistical significance

State correct hypotheses for a significance test about a population proportion or mean

Interpret p-values in context

Read pp. 529-535; problems 2, 12, 4, 14

42 9.1 Type I and Type II errors; the power of a statistical test

Interpret a Type I error and a Type II error in context and give the consequences of each

Understand the relationship between the significance level of a test, P(Type II error) and power

Read pp. 538-545; problems 15, 19, 21, 23, 25, 31, 32

43

9.2 Carrying out a significance test; the one sample z-test for a proportion; two-sided tests; why confidence intervals give more information

Check conditions for carrying out a test about a population proportion

If conditions are met, conduct a significance test about a population proportion

Use a confidence interval to draw a conclusion about a population proportion

Read Sec 9.2; problems 27-30, 41, 43, 45, 49, 51, 53, 55

44

9.3 Carrying out a

significance test for ; the one-sample t test; two-side tests and confidence intervals; inference for means: paired data; using tests wisely

Check conditions for carrying out a test about a population mean

If conditions are met, conduct a significance test about a population mean

Use a confidence interval to draw a conclusion about a population mean

Recognize paired data and use one- sample t procedures to perform significance tests for such data

Read Sec 9.3 57-60, 71-77 odd, 89, 94-97, 99-104

45

Chapter Review Read NTA pp 65-69 Special Problem 9 Portfolio 9.1-9.8


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Chapter 10 – Comparing Two Populations or Groups


46

10.1A Is yawning contagious? The sampling distribution of a difference between two proportions; confidence intervals for p1-p2

Describe the characteristics of the sampling distribution of �̂�1 − �̂�2

Calculate probabilities using the sampling distribution of �̂�1 − �̂�2

Determine whether the conditions for performing inference are met

Construct and interpret a confidence interval to compare two proportions

Read pp 601-611 13, 15, 17, 19, 22, 29-34

47

10.1B Significance tests for p1-p2; inference for experiments 10.2A Does polyester decay? The sampling distribution of a difference of two means

Perform a significance test to compare two proportions

Interpret the results of inference procedures in a randomized experiment

Describe the characteristics of the sampling distribution of �̅�1 − �̅�2

Calculate probabilities using the sampling distribution of �̅�1 − �̅�2

Read pp 611-621 15, 17, 21, 23 Read pp 627-632 29-32, 35, 37, 57

48

10.2 B The two-sample t statistic; confidence

intervals for 1-2; significance tests for

1-2; using two-sample t tests wisely

Determine whether the conditions for performing inference are met

Use two-sample t procedures to compare two means based on summary statistics

Use two-sample t procedures to compare two means from raw data

Interpret standard computer output for two-sample t procedures

Perform a significance test to compare two means

Check conditions for using two-sample t procedures in a randomized experiment

Interpret the results of inference procedures in a randomized experiment

Read pp 633-651 39-45 odd, 51, 53, 59, 65, 67, 70

49

Chapter Review Determine the proper inference procedure to use in a given setting

Read NTA 71-75 Portfolio 10.1-10.6

50



1/12/15

Chapter 11 – Inferences for Distributions of Categorical Data


51

11.1 The Candy Man. Comparing observed and expected counts; the chi-square statistic; the chi-square distributions and p-values; the chi-square goodness of fit test; follow up analysis

Know how to compute expected counts, conditional distributions, and contributions to the chi-square statistic

Check the Random, Large sample size, and Independent conditions before performing a chi-square test

Use a chi-square goodness of fit test to determine whether sample data are consistent with a specified distribution of a categorical variable

Examine individual components of the chi-square statistic as part of a follow-up analysis

Read Sec 11.1 1-11 odd, 17

52

11.2A Comparing distributions of a categorical variable; expected counts and the chi-square statistic; the chi-square test for homogeneity; follow up analysis; comparing several proportions


Use a chi-square test for homogeneity to determine whether the distribution of a categorical variable differs for several populations or treatments

Interpret computer output for a chi-square test based on a two-way table

Examine individual components of the chi-square statistic as part of a follow-up analysis

Show that the two-sample z test for comparing two proportions and the chi-square test for a 2 by 2 two-way table give equivalent results

Read pp 696-713 19-22, 27, 29, 31, 33, 35, 43

53

11.2B The chi-square test of association/ Independence; using chi-square tests wisely


Use a chi-square test of association/ Independence to determine whether there is convincing evidence of an association between two categorical variables

Interpret computer output for a chi-square test based on a two-way table

Examine individual component of the chi-square statistic as part of a follow-up analysis

Read pp 713- 723 45, 49, 51, 53-58

54

Chapter Review Distinguish between the three types of chi-square tests

Read NTA pp 77-81 Special Problem 11; Portfolio 11.1-11.7


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Chapter 12 – More About Regression


55

12.1 Helicopter Experiment; The sampling distribution of b, conditions for regression inference; estimating parameters; constructing a confidence interval for the slope; performing a significance test for the slope

Check conditions for performing inference

about the slope of the population (true) regression line

Interpret computer output from a least squares regression analysis

Construct and interpret a confidence interval

for the slope of the population (true) regression line

Perform a significance test about the slope of a population (true) regression line

Read Sec 12.1 1-19 odd

56

12.2 Transforming with powers and roots; transforming with logarithms

Use transformations involving powers and roots to achieve linearity for a relationship between two variables

Use transformations involving logarithms to achieve linearity for a relationship between two variables

Make predictions from a least-squares regression line involving transformed data

Determine which of several transformations does a better job of producing a linear relationship

Read Sec 12.2 21-26, 33-41 odd, 45-48

57

Chapter Review

Read NTA pp 83-88 Portfolio 12.1-12.7

58



1/12/15

Exam Review

Day Topics Homework

59

Review See Review Handout

60


61


62


4/18-4/26

Easter Break

63


64


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68


69 Review

See Review Handout

70 Review

See Review Handout

71 Review

See Review Handout

72 Review

See Review Handout

73 Review See Review Handout

74 Wed 5/13

AP EXAM

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