Wiki Page, Math 13 - Perez Sandbox : Module 16 - Introduction to Inference (1 of 2)

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2026-01-17T21:15:19-08:00

This is the beginning of Unit 7. Unit 7 includes Modules 16, 17, & 18. Unit 7 concludes with the Unit 7 Checkpoint at the end of Module 18.

This module introduces us to the logic of statistical inference–drawing conclusions about a population based on a sample. The rest of the course is devoted to different types of statistical inference.

Let’s look at how the remainder of the course relates to the Big Picture of Statistics.

Recall that we start a statistical investigation with a research question. The investigation proceeds with the following steps:

1. Produce Data: Determine what to measure, then collect the data. (Design an observational study or an experiment)

2. Explore the Data: Analyze and summarize the data.
(Use graphs, such as pie charts or histograms, and numerical summaries, such as percentages or means and standard deviations.)

3. Draw a Conclusion: Use the data, probability, and statistical inference to draw a conclusion about the population.
(This is our focus for the rest of the course.)

In the Big Picture of Statistics, we are about to start the last step: Inference. We use data from a sample to “infer” something about the population in this and the upcoming modules. Inference is based on probability.

EXAMPLE

At the end of April 2005, ABC News and the Washington Post conducted a poll to determine the percentage of U.S. adults who support the death penalty.

Research question: What percentage of U.S. adults support the death penalty?

Steps in the statistical investigation:

1. Produce Data: Determine what to measure, then collect the data.
The poll randomly selected a sample of 1,082 people from the population of U.S. adults. Each adult answered this question: "Do you favor or oppose the death penalty for a person convicted of murder?"

2. Explore the Data: Analyze and summarize the data.
In the sample, 65% favored the death penalty.

3. Draw a Conclusion: Use the data, probability, and statistical inference to draw a conclusion about the population.

Our goal is to determine the percentage of the U.S. adult population that support the death penalty. We know that different samples give different results. What are the chances that a sample reflects the opinions of the population within 3%? Probability describes the likelihood that a sample is this accurate, so we can say with 95% confidence that between 62% and 68% of the population favor the death penalty.

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