Sampling Methods and the Central Limit Theorem

Aug 09, 2012

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2. GOALS. Explain why a sample is the only feasible way to learn about a population.Describe methods to select a sample.Define and construct a sampling distribution of the sample mean.Explain the central limit theorem. Use the central limit theorem to find probabilities of selecting possible sa

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Sampling Methods and the Central Limit Theorem

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Presentation Transcript

1. Sampling Methods and the Central Limit Theorem Chapter 8

4.4 Sampling Distribution Models and the Central Limit Theorem

4.4 Sampling Distribution Models and the Central Limit Theorem. Transition from Data Analysis and Probability to Statistics. Sampling Distributions. Population parameter : a numerical descriptive measure of a population.

646 views • 40 slides

The Central Limit Theorem

The Central Limit Theorem. Honors Statistics Lesson 7.4. Objectives/Assignment. How to find sampling distributions and verify their properties How to interpret the Central Limit Theorem How to apply the Central Limit Theorem to find the probability of a sample mean. Introduction.

551 views • 33 slides

Sampling Methods and the Central Limit Theorem

Sampling Methods and the Central Limit Theorem. Chapter 8. GOALS. Explain why a sample is the only feasible way to learn about a population. Describe methods to select a sample. Define and construct a sampling distribution of the sample mean. Explain the central limit theorem .

2.27k views • 21 slides

Central Limit Theorem

Central Limit Theorem. The central limit theorem and the law of large numbers are the two fundamental theorems of probability.

954 views • 39 slides

The Central Limit Theorem

The Central Limit Theorem. The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample mean approaches a normal distribution as the sample size increases.

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Chapter 10: Sampling and Central Limit Theorem

Chapter 10: Sampling and Central Limit Theorem. Number of Cards : 52 Excluding Jokers Unit of analysis = 1 card Denominations : 13 2-10 Ace (1) Jack Queen King. Colors : 2 Black (26 cards) Red (26 cards) Suits : 4 Clubs ( ♣ ) Diamonds ( ♦ ) Hearts ( ♥ ) Spades ( ♠ ).

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Central Limit Theorem

Central Limit Theorem. Different Populations Same Results.

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The Central Limit Theorem

The Central Limit Theorem. For simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution of the sample means is approximately normally distributed. The Central Limit Theorem.

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Central limit theorem

Gaussians everywhere. Central limit theorem. Gaussians in physics. Slightly-disguised Gaussians in biology. 0. 1. -1. 0. Central limit theorem. H. T. -3. -2. -1. 0. 1. 2. 3. Gaussians everywhere. Central limit theorem. Gaussians in physics.

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Central Limit Theorem

Central Limit Theorem. Example: (NOTE THAT THE ANSWER IS CORRECTED COMPARED TO NOTES5.PPT) 5 chemists independently synthesize a compound 1 time each. Each reaction should produce 10ml of a substance.

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THE CENTRAL LIMIT THEOREM

THE CENTRAL LIMIT THEOREM. The World is Normal Theorem. Sampling Distribution of x- normally distributed population. n=10. Sampling distribution of x: N (  ,  /10). /10. Population distribution: N(  ,  ). . Normal Populations. Important Fact:

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Sampling Methods and the Central Limit Theorem

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The Central Limit Theorem

The Central Limit Theorem. Paul Cornwell March 31, 2011. Statement of Theorem.

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Central Limit Theorem

Central Limit Theorem. General version. Statistics are. Unbiased : on average, the calculated statistic from a random sample equals in value to the corresponding population parameter.

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5.4 Sampling Distributions and the Central Limit Theorem

5.4 Sampling Distributions and the Central Limit Theorem. Find sampling distributions and verify their properties Interpret the Central Limit Theorem Apply the Central Limit Theorem to find the probability of a sample mean. Sampling distribution.

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Sampling Distributions & the Central Limit Theorem

Sampling Distributions & the Central Limit Theorem. A sampling distribution is a distribution consisting of a particular sample statistic from a collection of samples of the same size (n) that are repeatedly taken from a population.

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Central Limit Theorem

Central Limit Theorem. Given:. 1. The random variable x has a distribution (which may or may not be normal) with mean µ and standard deviation  . 2. Samples all of the same size n are randomly selected from the population of x values. Central Limit Theorem. Conclusions:.

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Sampling Distribution and the Central Limit Theorem

Sampling Distribution and the Central Limit Theorem. Sampling Distributions – Sample Means. Instead of working with individual scores, statisticians often work with means. Several samples are taken, the mean is computed for each sample, and then the means are used as the data,

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THE CENTRAL LIMIT THEOREM

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Central Limit Theorem

Central Limit Theorem The theorem states that the sum of a large number of independent observations from the same distribution has, under certain general conditions, an approximate normal distribution.

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The Central Limit Theorem

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Sampling Methods and the Central Limit Theorem

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Presentation Transcript

4.4 Sampling Distribution Models and the Central Limit Theorem

The Central Limit Theorem

Sampling Methods and the Central Limit Theorem

Central Limit Theorem

The Central Limit Theorem

Chapter 10: Sampling and Central Limit Theorem

Central Limit Theorem

The Central Limit Theorem

Central limit theorem

Central Limit Theorem

THE CENTRAL LIMIT THEOREM

Sampling Methods and the Central Limit Theorem

The Central Limit Theorem

Central Limit Theorem

5.4 Sampling Distributions and the Central Limit Theorem

Sampling Distributions &amp; the Central Limit Theorem

Central Limit Theorem

Sampling Distribution and the Central Limit Theorem

THE CENTRAL LIMIT THEOREM

Central Limit Theorem

The Central Limit Theorem

Sampling Methods and the Central Limit Theorem

Sampling Distributions & the Central Limit Theorem