Sampling Distributions - Means AP Stats - Chapter 18 Part 2 Up to this point in the chapter we have been working with sampling distributions for proportions. Well, the concepts of sampling distributions works for sample means as well. The Central Limit Theorem

There are two properties of "The Central Limit Theorem" that we need to remember in order to use it. The mean of a sampling distribution will be equal to the population mean.

A sampling distribution can be approximated by a Normal model. Just like with sampling distributions for proportions, when working with sample MEANS, you need to define the mean of your Normal model and the standard deviation of your Normal model. The mean of the Normal model for x-bar is equal to the population mean. The standard deviation of the sampling distribution for means is . . . Try this . . . Human gestation times have a mean of about 266 days, with a standard deviation of about 16 days. Suppose we look at the average gestation times for a sample of 100 women. if we imagined all the possible random samples of 100 women we could take and looked at the histogram of all the sample means . . .

1. what shape would it have?

2. where would the center of that histogram be?

3. what would be the standard deviation of that histogram? 1. It would be Normal shaped.

2. The center would be at 266 days.

3. SD = 16/sqrt 100 = 1.6 days The Assumptions and Conditions you must check to use a Sampling Distribution for Means are the similar as those for proportions, but just a little bit different. Randomization Condition - Same

Independence Assumption or 10% Condition - You must assume that the observations are independent, but if you cannot make that assumption, you must check the 10% condition.

Large Enough Condition - We will talk about this condition more in Chapter 24, but for now we will just assume that our sample is large enough. Now let's look at an example problem One Last Topic We don't always have the population standard deviation or the population proportion. If we don't have them, then we can use the sample proportion or sample standard deviation to estimate the standard deviation of the sampling distribution. This is called STANDARD ERROR. Read pgs 424 and 425 for more information. Just for fun . . . See you in stats class.

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# Sampling Distributions - AP Stats Chapter 18 Part 2

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