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)

Chapter 10 Comparing Two Populations

AP Statistics Standards

IV. Statistical Inference: Confirming models

A. Confidence intervals

1. The meaning of a confidence interval
2. Large sample confidence interval for a proportion

B. Tests of significance

1. Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power
2. Large sample test for a proportion
3. Large sample test for a mean
4. Large sample test for a difference between two proportions

 Objectives
 Essential Question: How does a confidence interval for proportions compare to one for means?

Inference for Proportions

1. State the meaning of p-hat. A statistic estimating a population proportion

 p-hat = count of successes in sample count of observations in sample
1. Calculate the mean and standard deviation of a binomial distribution.

 Data Type Mean Std Dev count or number np [np(1 - p)]^0.5 proportion p [p(1 - p) / n]^0.5
1. Be aware that a binomial distribution (the distribution typically used for analyzing proportions) is essentially a sampling distribution. Note that as a sampling distribution, when the sample size is large enough (see below), the distribution begins to resemble a normal distribution.

2. When appropriate, correctly model a binomial distribution as a normal distribution if the 2 conditions shown below are met.

 np ≥ 10 n(1-p) ≥ 10
1. Create a confidence interval for a proportion based on single large  sample  (p.689).

Conf. Int. = est. ± ME

ME = Z* [p(1 - p) / n ]0.5

1. Perform a hypothesis test comparing a single large sample proportion (p-hat) against a know population proportion (p). Note, this is a z-test.

 Z = (p-hat) - p [p(1-p)/n]0.05

Homefun (formative/summative assessment):  --

 Essential Question: Assuming an SRS and given equal sized margins of error, is the sample size required to survey the entire United States substantially larger than the one for conducting the same survey in Greenville SC?

Two-Sample Proportions

1. Calculate the desired sample size for a given margin of error in a proportion (p. 696). Remember that p = 50% will give the max sample size and hence most conservative estimate of the size needed. Using the equation for margin of error, solve for n.

Relevance: Survey results are a ubiquitous feature of newspaper and magazine articles as well as political arguments. The above is the basic way that surveys are designed.

1. Create a confidence interval for comparing two sample proportions.
2. Margin of Error for Confidence Interval
 ME = z* [ p̂1(1-p̂1) /n1 + p̂2(1-p̂2) /n2 ]0.5

3. State the Ho used for comparing two sample proportions.

Ho: p2 - p1 = 0

or

Ho: p2 = p1

1. Calculate the pooled portion of successes using both samples. Pooled tests are generally run when testing 2 proportions because the subjects are typically selected from a common pool but receive different treatments--example: drug tests, heart attacks vs. fat in diet, accident rate vs. drunkenness, etc. In all these examples, the human subjects are typically drawn from the same population.

 pc = count of successes in both samples combined count of observations in both samples combined = X1 + X2 n1 + n2

1. Perform a hypothesis test for comparing two sample proportions. Note: the TI-83 calculator automatically does a pooled test when the 2-PropZTest option is selected

Test Statistic for  Hypothesis Testing
 z = (p̂1- p̂2) - 0 [ p̂c(1-p̂c) /n1 + p̂c(1-p̂c) /n2 ]0.5

Homefun (formative/summative assessment): Read 10.1, Exercises 1, 3, 7, 9, 13 pp. 621 to 623

 Essential Question: How What is the standard error (standard deviation of the sampling distribution) for the difference between 2 means when population std deviations are known?

1. State that the sampling distribution mean for the difference between samples drawn from two different populations is the same as the difference between the the two population means.

In other words,

the mean of the sampling distribution for ( x-bar1 - x-bar2 ) is ( μ1 - μ2 )

2. Given the standard deviations of 2 different populations, calculate the standard error for the sampling distribution of the difference between the two means.
 SE = ( σ12/ n1 + σ22/ n2 ) 0.5

Homefun (formative/summative assessment): Read 10.2, Exercises 35, 37 p. 652

 Essential Question: How can you determine if 2 populations differ if at the start you have no information?

Two-Sample t-Test

1. State the assumptions made for two-sample tests. (p. 650)

SRS used for generating the sample

independent - matched pairs violate independence

normally distributed population

2. Create confidence intervals and hypothesis test using two sample t procedures assuming that the sigmas of the two populations are unequal. This is the most conservative assumption.

Ho: μ1 - μ2 = 0  but can also be written, Ho: μ1 = μ2

Test Statistic for  Hypothesis Testing Margin of Error for Confidence Interval
 t = (xbar1 - xbar2) - 0 (s12/n1 + s22/n2)0.5
 ME = t* (s12/n1 + s22/n2) 0.5

1. Create confidence intervals and hypothesis test using two sample t procedures and the most conservative method of determining df.

df = (the lower of n1 -1 or n2 - 1)

1. Be aware of the more accurate way to calculate df as is done by the TI-83 calculator. This method can return a df that includes a decimal fraction. For example: df = 12.37

2. Perform two sample hypothesis t-procedures on the TI-83.

3. State the key assumption required for using the pooled two-sample t-procedures. This is the method is an option in the TI-83 calculator.

The sigmas of the two populations are the same

Homefun (formative/summative assessment): Exercises 39, 43, 47, 45, 67, 69, 71, 75 pp. 652 to 660

Chapter 10 AP Statistics Practice Test multiple choice and free response pp. 664 to 666

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