9.3

9.3 Sample Means

To Know!

Sample means are just averages of observations, so they are among the most common statistics used.
Averages are less variable and more normal.
sample xbar is an unbias estimator of Mu.
Mu of Xbar = the population Mu.
The Standard deviation of Xbar = the standard deviation of the population divided by the square root of the total number.

Key Concept!

Central Limit Therom

Just remember - The more samples you have and the more in the samples the more normal of a curve you will get. Also see vocab for straight info on what it exactly is. There is an awesome applet at the website at www.whfreeman.com/statistics It will be in chapter nine's applets. Check it out!

When we talk about sample means is good to understand what kind of questions we are looking for. Here are a couple which we are looking for in this section.

What is the average household income?
What is the average blood pressure for a 50 yr old man?
What is the average GPA of PSHS Seniors?

Heres a sample problem.

    The mean height of women is Mu=64.5 with standard deviation of 2.5
What is the probability that a mean height of a SRS of 10 women is greater than 66.5in?
            X>=66.5= P(Z>= 66.5 -64.5
                                               2.53
                                     Square root of 10   ) = 2.53
So Z=2.53 and using table A we can see that there is .57% on getting a sample this weird or weirder. So we could say that there is indeed some evidience that the actual mean may be higher than that.
Great Job if you understood that problem.
    You are now masters of chapter nine!

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