Mr. Rogers - AP Statistics Objectives
Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
  Probability Binomal Distr Sampling Distr Conf Intervals
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

  1. Sampling distribution of a sample proportion

  2. Sampling distribution of a sample mean

  3. Central Limit Theorem

  4. Sampling distribution of a difference between two independent sample proportions

  5. Sampling distribution of a difference between two independent sample means

  6. Simulation of sampling distributions

 

Objectives

Essential Question: Can we describe the shape of a distribution made up of many means from samples of the same size even without knowing what the population's  distribution's shape is like?

Ch

  1. Describe the difference between a parameter and a statistic and give examples.

  2. Explain the use of p and p-hat.

  3. Given a sampling distribution, explain its meaning.

  4. Determine if a statistic is unbiased.

Unbiased: sampling distr. mean = pop. mean

  1. Compare variability to bias .

Essential Question: Which is worse, variability or bias?

  1. State how the variability of a statistic changes relative to population size. Population size has no effect as long as the population size is significantly larger than the sample size. By contrast, a larger sample size reduces variability.

  2. State which distribution typically has less variability, a sampling distribution or the population distribution it is based on? It's the sampling distribution.

  3. Calculate standard error.

(standard error) =  (σ of sampling distr.)

                           =  (σ of population) / (n^0.5)

 

Homefun (formative/summative assessment)

Read section

 

 

Stats Investigation: Central Limit Theorem

Purpose: Does the variability in the sampling distribution actually decrease as predicted by the central limit theorem?.

Instructions: Go to http://intuitor.com/statistics/CentralLim.html and read the write up. Open the Central Limit Theorem Applet and set the number of samples slider to its maximum (max=2010). Run at least 10 simulations using a variety of sample sizes from 1 to 100. From the sampling distribution plot, record the sample size, standard deviation, and standard error.

Analysis 1: Make a scatter plot of standard deviation vs. sample size. Perform linear regression and power regression on the data in the plot. Also make a residual plot for both forms of regression.

Analysis 2: Make a second scatter plot of standard deviation vs. standard error. Perform linear regression, report the r-square value, and make a residual plot for this data.

Questions /Conclusions:

  1. Which regression equation best fits the data in Analysis 1? Explain why?
  2. Explain the r-square value for the most appropriate equation in analysis 1.
  3. What is the predicted equation in analysis 2 and how does it compare to the regression equation.
  4. In analysis 2, what is the difference between the standard deviation of the sampling distribution and the standard error. Why do they have almost identical values?
  5. What is the difference between sample size and number of samples. Describe how increasing them influences the sampling distribution.
  6. What is the difference between the central limit theorem and the law of large numbers.

Ch 9

  1. Calculate the mean and standard deviations of a binomial distribution for proportions.

  2. Compare the binomial distributions for proportions to the binomial distributions for counts.

Data Type Mean Std Dev
count np [np(1 - p)]^0.5
proportions p [p(1 - p) / n]^0.5
  1. State why the binomial distribution is basically always a sampling distribution. n represents the size of a sample drawn from a population.

  2. State the three rules of thumb which must be met before using the normal approximation of the binomial distribution (pp. 506 & 507). Note: on an AP Stats Exam, always  demonstrate that these 3 rules are met before using a normal distribution approximation of the mean.

population   > 10n

np  > 10

n(1-p) > 10

  1. State how the central limit theorem applies to sampling distributions.

  • larger sample size → less variability

  • larger sample size → closer to N-distr.

Relevance: The central limit Theorem is one of the 2 foundation stones that statistics rests on, the other being the Law of Large Numbers.

  1. A sampling distribution made up of a large number of samples will have a mean very close to the population mean and a standard deviation very close to (σ of population) / (n^0.5)

Homefun (formative/summative assessment):

--  Read section

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