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Classroom Resources > Against All Odds: Inside Statistics > 26. Small Sample Inference for One Mean

Mathematics

9-12, College/Adult

Against All Odds: Small Sample Inference for One Mean Transcript

Student Guide

Faculty Guide

Statistics is the art and science of gathering, organizing, analyzing and drawing conclusions from data. And without rudimentary knowledge of how it works, people can't make informed judgments and evaluations of a wide variety of things encountered in daily life.

As a first step in visualizing data, we use stemplots to understand measurements taken by the U.S. Army when they size up soldiers in order to design well-fitting gear and supplies for modern warfighters.

Meteorologists use histograms to map when lightning strikes and this visualization technique helps them understand the data in new ways.

It's helpful to know the center of a distribution — which is what the clerical workers in Colorado Springs found out in the 1980s when they campaigned for comparable wages for comparable work. Mean and median are two different ways to describe the center.

Using the example of hot dog calorie counts, we use boxplots to visualize the five-number summary and make comparisons between different types of frankfurters.

How can we compare sales at two franchises in the Wahoo's restaurant chain? Standard deviation helps us quantify the variability in sales.

A nature preserve that's tracked bird migrations through New England for decades records tons of bird-related data; everything from wingspan measurements to arrival dates provides examples of normal distributions.

Visit the Boston Beanstalks club for tall people. Height is normally distributed and we can use membership cutoffs and population data to calculate z-scores.

Production at Pete and Gerry's Organic Eggs provides a number of distributions that look normal — but are they?

Plotting annual numbers of Florida powerboat registrations and manatee killings suggests an uncomfortable relationship for the marine mammals.

Winter snowpack in the Colorado Rockies can predict spring water supply. Plotting annual measurements in a scatterplot lets resource managers draw a regression line that helps them forecast water availability.

Twin studies track how similar identical and fraternal twins are on various characteristics, even if they don't grow up together. Correlation lets researchers put a number on it.

One city surveyed the happiness of its residents. Two-way tables help organize the data and tease out relationships between happiness levels and opinions about aspects of the city itself.

This historical story describes how researchers untangled the relationship between smoking and lung cancer.

We move beyond observational studies — like one of marine life in the remote Line Islands — to designing experiments that manipulate various subject groups — as in the case of a medical study about osteoarthritis treatments.

The U.S. counts every resident every ten years — or at least tries to. Statisticians use sampling from a population as an alternative to a complete count, as utilized at a potato chip factory.

A visit to the University of New Hampshire Survey Center illustrates how pollsters create accurate surveys. They can then use details from their sample to make inferences about a whole population.

Probability is the mathematics of chance behavior — and can help predict events such as the daily weather, or whether an asteroid will collide with Earth.

Casinos are as well versed in probability as statisticians and probability models help them maintain the house advantage over gamblers.

The Challenger space shuttle disaster was blamed on faulty O-rings. How can probability calculations on random variables help predict the chances of this kind of failure?

Sickle cell disease is an example of binomial distribution in families with two parents who are carriers for this genetic trait.

Heights of third graders in one class. Quality scores for circuit boards at a factory. Taking multiple samples allows us to visualize the sampling distribution of the sample mean.

This quality control method helped Quest Diagnostics streamline and improve their system for processing and testing lab samples so they could meet their nightly deadlines.

A battery manufacturer tests just a sample of its product to verify its claims about battery life. A margin of error and a confidence level help quantify its accuracy.

Is a newly-discovered poem really written by William Shakespeare? Using statistical analysis of his known word use, researchers set up null and alternative hypotheses to investigate.

A brewer uses this technique to monitor quality differences in multiple batches of the same beer.

Comparing the activity and calorie expenditure levels of Western office workers and African hunter gatherers adds some surprising new data to the science of obesity.

Managers have no clue what conditions actually motivate their workers best, as shown by research conducted by Teresa Amabile, host of the original Against All Odds.

Host Dr. Pardis Sabeti's own research examines possible genetic resistance to deadly Lassa fever in West Africa. Using Inference for Two-Way Tables helps untangle potential relationships.

Historical story of how statisticians built the case against DDT as the culprit behind plummeting peregrine falcon population numbers.

Does holding a heavier clipboard make you estimate that a jar of coins has more money in it than if you're holding a lighter clipboard? Psychologists use One-Way ANOVA to analyze the data from this experiment.

This review of the course through the preceding 31 video modules provides an overview of the practice of statistics and helps students appreciate how statistical methods can help them better understand their world.

The Stemplots tool organizes data — either your own input or randomly generated — into a stemplot.

The Wafer Thickness tool generates data (represented as a histogram)

The Control Chart interactive allows the user to play the role of a semiconductor quality control manager