Mr. Rogers - AP Statistics Objectives
Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Hypothesis Testing- Multi-Sample Testing Chi Test Regression Testing  
Unit Plan Practice Test
Latin

Latin/Greek Root Words

arch--------->ancient, example: archtype;         chrono------>time, example: chronology;             -dom----------->quantity/state, example: freedom               fer-------->carry, example: transfer;               gen--------->birth, example: generate;                 luc-------->light, example lucid;                 neo--------->new, example: neonatologist;                olig--------->few, example: oligarchy;              omni--------->all, omniscient;            sym--------->together, symbol;

(Statistics connection)

AP Statistics Standards

III. Anticipating Patterns: (continued)

D. Sampling distributions

8. Chi-square distribution

IV. Statistical Inference:

B. Tests of significance

  1. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables)

Objectives

Essential Question: Why would it be useful to have a quantitative way to test if data fits a particular distribution instead of merely relying on histograms, box plots, or normal quantile plots?

Ch. 13.1 Inference for Tables

  1. Name 2 instances when a chi-squared test can be used. Note: chi is pronounced kie (rhymes with pie).
    • Goodness-of-fit (tests the Ho that there is no difference between the distribution of sample data and a known distribution ) example
    • Inference for 2-way tables (tests the Ho that there is no relationship between row and column variables)
  1. Describe the shape and range of the chi-squared distribution. Skewed right, zero to positive infinity

  2. Determine degrees of freedom for a goodness-of-fit chi squared calculation. ( df = n-1)

  3. Calculate the chi squared statistic.

C2 = S (O - E)2 / E

Where:

O = observed data point

E = expected

  1. Perform chi squared goodness of fit hypothesis tests.

Assumptions:

Simple Random Sample

Independence: Observations are assumed to be independent. Chi-squared can't be used to test correlated data (like matched pairs or panel data).

 

  1. Note that the hypotheses for a chi-squared test cannot readily be stated mathematically. They are as follows:
  • Null hypothesis: The data's distribution and the reference distribution are the same.
  • Alternative hypothesis: The data's distribution and the reference distribution are different.

 

  1. Find p-values for a chi squared test using both the table and the TI - 83 calculator

    Χ2 cdf ( LUD ). Lower, Upper, Degrees of freedom

Homefun:  -- Read 11.1, Exercises 1, 3, 11, 13, 19, 21 pp.692 to 695

 

Essential Question: How can statistics be applied to genetic analysis in the real world?
  1. Describe how the chi-squared test can be used for determining if a set of data is not randomly distributed assuming that all events are equally probable.

 

Stats Investigation: statistical Analysis of Genome Data - computer lab using Minitab. 

Essential Question: How can tables containing massive amounts of data be rapidly screened for relationships between the rows and columns?

Ch. 13.2  Inference for Two-Way Tables

  1. Calculate expected results for tables (p.720 ).

expected = 

 ( row total ) ( column total )

(table total)

  1. Calculate chi-squared statistics for tables (p. 723).
  2. Determine the degrees of freedom for a chi-squared (p. 724).

df = (rows-1)(columns-1)

  1. Perform hypothesis tests using chi-squared statistics.
  2. Be able to read chi-squared computer print outs.

 

Homefun:  -- Read 11.2, Exercises 33, 35, 37, 43, 45, 51 pp. 725 to 729

Chapter 11 practice test multiple choice and free respnse, pp. 733 to 735

 

The Practice of Statistics, Yates, Moore, McCabe

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