Sampling Distributions. Essential Question: How is the mean of a sampling distribution related to the population mean or proportion?

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Presentation transcript:

Sampling Distributions

Essential Question: How is the mean of a sampling distribution related to the population mean or proportion?

Introduce In groups of 5-6: Answer the following question How long (in minutes) does it take you to get to school in the morning? Calculate sum and the mean of the responses in your group

Line Plot: What do you think the Class mean will be based on the Sample Distribution?

Calculate the class Mean Group A Total: Number of Members: Group B Total: Number of Members: Group C Total: Number of Members: Group D Total: Number of Members: Group E Total: Number of Members: Group F Total: Number of Members: Total: ___________ Total: ___________ Class Mean:

Developing a Sampling Distribution

WORK IN PAIRS! Using Random Number Generator, produce a sample of 5 gym members. Find the mean age for your sample. (round to the nearest tenth)

Calculate

WORK IN PAIRS! Using Random Number Generator, produce a sample of 15 gym members. Find the mean age for your sample. (round to the nearest tenth)

Reflect In the class histograms, how does the mean of the sample means compare with the population mean? What happens to the standard deviation of the sample means as the sample size increases? What happens to the shape of the histogram as the sample size increases?

Sampling Distribution

3 is known as the CENTRAL LIMIT THEOREM

Boxes of Cruncho cereal have a mean mass of 323g with a Standard Deviation of 20g. You choose 36 boxes of cereal at random.

The sampling of the sample mean is approximately normal.

Boxes of Cruncho cereal have a mean mass of 323g with a Standard Deviation of 20g. You choose 36 boxes of cereal at random.

Reflect When you choose a sample of 36 boxes, is it possible for the sample to have a mean of 315g? Is it likely? Explain.

Sample Proportions Sampling Distribution

5 samples 10 samples

Reflect How can you find the interval that captures 99.7% of the sample proportions? How likely is it that a random sample of 50 students includes 31 students who live off campus? Explain