Wiki Page, Math 13 - Perez Sandbox : Big Picture of Statistics Step 4: Inference for Population Means

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2026-01-17T21:14:52-08:00

A statistical study can be divided into four steps.

1. Producing Data. A sample is selected from a population (Unit 6)

2. Exploratory Data Analysis (Units 2, 3, 4)

3. Probability (Unit 5)

1. See the data in relation to random samples from the population.

2. How much variability in random samples from this population?

3. Model variability with a Normal curve (when does this work?)

4. When we don't know the population mean or standard deviation, we will develop a new type of model. (This is new to us in this module.)

4. Inference (Units 7, 8, 9, 10, 11)

Estimate a Population Parameter: Calculate a Confidence Interval for a Population Mean (or a Difference Between Two Population Means)--this is new to us in this module--and state a confidence level to describe the probability that a random sample estimates the population mean (or the difference between two population means) with this margin of error.

Test a Claim about a Population Parameter: Conduct a hypothesis test about a Population Mean (or about a Difference Between two Population Means)--this is new to us in this module. State a hypothesis about a population mean (or the difference between two means). Find a P-value. What is the probability that random samples have means that vary more from the population mean than that data? The smaller the probability, the stronger the evidence against the claim.