Sampling Distributions Essential Question How is the mean

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: • Group B Total: • Group C Total: • Group D Total: • Group E Total: • Group F Total: ______ Class Mean: Number of Members: Number of Members: Total: ______

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 323 g with a Standard Deviation of 20 g. 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 323 g with a Standard Deviation of 20 g. 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 315 g? 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