Statistics– Notes and Examples



Statistics– Notes and Examples Name:

Section 8-1 Distribution of Sample Mean Date: Hour:

If we wanted to estimate the mean income of the U.S. households, we could survey a random sample of U.S. households and use the results of the survey to estimate the mean household income. This is an example of where you use a sample to draw a conclusion about a population.

Example: One semester, Prof. Goehl had a small statistics class of seven students. He asked them the ages of their cars and obtained the following data:

2, 4, 6, 8, 4, 3, 7

Construct a sampling distribution of the mean for samples of size n = 2. What is the probability of obtaining a sample mean between 4 and 6 years, inclusive that is, [pic].

Solution: If n = 2 then there are [pic] samples that can be made.

[pic]

The Sample Distribution of the Mean is…

[pic]

Draw a histogram of the sample means:

So we can compute

[pic]

Compute the mean and standard dev. of the sample means using a calculator.

= mean

= St.Dev

Check out



So there is less in the distribution as the sample size increases. As the sample size increases the .

So back to our earlier example…

[pic] and [pic]

Assignment: Lesson _________ , p. ________________ , #________________

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[pic]

The Law of Large Numbers says

To find the mean ([pic]) and standard deviation ([pic]) of a large sample set

[pic] and [pic]

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