Mrudulla Gnanadesikan

An Activity-Based Statistics Course

So that students can acquire a conceptual understanding of basic statistical concepts, the orientation of the introductory statistics course must change from a lecture-and-listen format to one that...

The Law of Large Numbers and the Central Limit Theorem

When pollsters ask a question such as “Do you approve of the job performance of the president?” they usually take large samples. They expect the sample percentage to be close to the population percentage, but they are never certain if their results are accurate. likewise, suppose you toss a coin over and over again and keep track of the percentage of heads obtained along the way. You expect to get heads half of the time, but that doesn’t mean that you’ll get exactly 50 heads in the first 100 tosses. As the number of tosses goes up, you expect the sample percentage to approach 50%, but there will be variability.

The Regression Effect

Amathematics supervisor in a large U.S. city got a grant to improve mathematics education. She tested all students and placed those with the lowest achievement scores in a special program. After a year, she retested them and was gratified to see that the students in the special program improved in comparison with the rest of the students.

Confidence Intervals for the Percentage of Even Digits

Suppose a political poll says that 56% of voters approve of the job the president is doing and that .this poll has a margin of error of 3%. The 3% margin of error results from the fact that the poll was taken from a sample of voters. Since not all voters were included, there is some error due to sampling, or sampling error. If all voters had been asked, the polling organization predicts that the percentage would have been in the confidence interval of 53% to 59%. For every 100 polls that report a 95% confidence interval, the polling organization expects that 95 of the confidence intervals will contain the true population percentage. In this activity you will take a “poll” of random digits in order to estimate the percentage that are even.

Theme: Sample Survey

Your college administrators want to know how many students will want parking spaces for automobiles next year. How can we get reliable information on this question? One way is to ask all of the returning students, but even this procedure would be somewhat inaccurate (why?) and very time consuming. We could take the number of spaces in use this year and assume next year’s needs will be about the same, but this will have inaccuracies as well. A simple technique that works very well in many cases is to select a sample from those students who will be attending the school next year and ask each of them if they will be requesting a parking space. From the proportion of “yes” answers, an estimate of the number of spaces required can be obtained.

Streaky Behavior: Runs in Binomial Trials

When they have made several baskets in succession, basketball players are often described as being “hot.” When they have been unsuccessful for a while, they are described as being “cold” or “in a slump.” Fans and basketball players alike tend to believe that players shoot in streaks.

Models, Models, Models…

When looking at relationships between two quantities, we are often interested in fitting a mathematical function to describe this relationship. Statisticians call these functions models. This activity uses data on levels of carbon dioxide in the atmosphere at a site in Hawaii to illustrate fitting a model to data. Carbon dioxide, or CO2, is one of the gases in the environment whose levels have been increasing. Why should this be of great interest? It is so because scientists are concerned that in creasing levels of complex gases, one of which is CO2, will thicken the blanket around the Earth and prevent heat from escaping. This could result in “global warming,” which could lead to disastrous coastal flooding and severe droughts. These data have been used by scientists in studies involving levels of CO2 in the atmosphere. Reasons for the choice of the site, and additional information regarding the data, are shown after the activity. The patterns observed in this data can be considered to be typical of what could be observed globally.

Let Us Count

We all know that when we repeat an action we may not get the same result. An athlete may not run a mile in the exact same time twice, you may not get the same number of french fries in two orders at McDonald’s, or two scoops of ice cream will not be exactly the same. Therefore, “variability” is present in the outcomes of all repeated actions. Process variability, where measurement plays a role, is a major concern in the real world. The main objective in process control is to identify the sources of variation and look for ways to control the variation.

Predictable Pairs: Association in Two-Way Tables

The results of a survey might provide lots of information on characteristics of students at your school, such as what proportion eat breakfast regularly, like first-period classes, have a job, or own a car. Does a “yes” response to one of these characteristics help us predict what the response of that same person will be to another characteristic? Is a person who eats breakfast likely to have an early class? Is a person who has a job likely to own a car? Looking for associations between categorical variables is an important part of the analysis of frequency data. How to begin the process of measuring association is the subject of this lesson.

Is Your Shirt Size Related to Your Shoe Size

The great painter and scientist of the fifteenth century, Leonardo, studied the human body and pro vided detailed accounts of the relationships among various body parts. Leonardo’s work on how the size of one part is related to that of another was for the purpose of instructing painters on how to paint the human body, but some of these relationships are of practical interest as well. (Who might be interested in the relationship between arm length and circumference of the neck, for example?) In this activity we will investigate the accuracy of some of Leonardo’s pronouncements by modeling relationships between the sizes of various body parts.