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- Statistics 201
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- Ch 18 (part 1) - Sampling Distribution Models

Megan R.

Population

The set of all the objects or people we wished we had data on

Sample

Set of all the objects or people we actually have data on

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p

= population proportion

We wish we had this, but we only could if we polled ALL US adults, for example.

We wish we had this, but we only could if we polled ALL US adults, for example.

p hat

= sample proportion

This is what we actually have...just a sample of the population.

This is what we actually have...just a sample of the population.

Standard deviation of phat

The difference between what we measure and what is known/the truth

= sqrt [ (pq)/n ]

= sqrt [ (pq)/n ]

When using a model for the distribution of sample proportions, you make two assumptions. Those are:

- the independence assumption and the sample size assumption

These are things you want to be true, but you can't really check them so you just have to assume.

These are things you want to be true, but you can't really check them so you just have to assume.

The Independence Assumption

The sampled values must be independent of each other.

The Sample Size Assumption

The sample size, n, must be large enough.

Before using the Normal Model to model the distribution of sample proportions we need to check 3 conditions. Those are:

The Randomization Condition, the 10% Condition, and the Success/Failure Condition

Randomization Condition

The sample should be a simple random sample of the population.

The 10% Condition

The sample size, n, must be no larger than 10% of the population.

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The Success/Failure Condition

The sample size has to be big enough so that both np and nq are at least 10.

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