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

Mean = 41.2Standard Deviation : 15.3

• 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

• Shows you how a particular statistic varies across all samples of n individuals from the same population.

• Sample Mean • Sample Standard Deviation (standard error of the mean)

• You may notice that is close to regardless of sample size.

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.

• What is the probability that your sample has a mean mass of at most 325g?

_________ = ______

= _________ = = ______

= _________

The sampling of the sample mean is approximately normal. •Convert 325 to a z-score.

______

Use the standard normal table to find the probability. = _______

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

• What interval captures 95% of the means for random samples of 36 boxes.

- ______ - 2(_____) = _______

+ ______ + 2(_____) = _______

Therefore, 95% of the sample means fall between ________ and ________.

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