# Math 119: Fundamental Statistics

## Welcome to the MTH 119 Course Design Toolkit

Course description: This course provides a survey of statistical methods, with examples taken from sociology, psychology, education, and related fields. A minimum background in mathematics is assumed. Topics include descriptive statistics, measure of central tendency and variability, probability, binomial and normal distributions, estimation, correlation, and regression.

# Introductory Remarks

Students generally take MTH119 as a requirement for their program, though a few programs offer a choice between this course and MTH125 Modern College (Liberal Arts) Mathematics. They can be nervous about taking a statistics course because of their own history with mathematics courses and because of the general feeling about statistics being a difficult mathematics course.

Some approaches to lessen their anxiety should be considered before the first class and in the first weeks. You can plan to have some assessments that are low stakes and allow students to practice statistics before an exam. These could include online homework (such as MyMathLab ) that allow students several tries at an answer and online help and support. You could also have frequent very brief quizzes. This allows students to see their errors quickly, encourages attendance and encourages students keeping up with the material. Some instructors offer outside assignments to allow students to practice statistics and work through their thought process as they engage in the material. They might design survey questions or draw graphs of real data.

Another practice that also encourages students in the early weeks of the class is to show a sense of humor with stories and jokes and relating the material to known concepts. (We all know the example of how correlation is not causation: Eating ice cream is strongly correlated to shark attacks.)

When learning statistics, there are three areas of focus. These definitions of statistical literacy, thinking and reasoning are from the Artist Website. (Find out more in the Resources section.)

Statistical literacy involves understanding and using the basic language and tools of statistics: knowing what statistical terms mean, understanding the use of statistical symbols, and recognizing and being able to interpret representations of data. To read more about statistical literacy see Rumsey (2002).

Statistical reasoning is the way people reason with statistical ideas and make sense of statistical information. Statistical reasoning may involve connecting one concept to another (e.g., center and spread) or may combine ideas about data and chance. Reasoning means understanding and being able to explain statistical processes, and being able to fully interpret statistical results. To read more about statistical reasoning see Garfield (2002).

Statistical thinking involves an understanding of why and how statistical investigations are conducted. This includes recognizing and understanding the entire investigative process (from question posing to data collection to choosing analyses to testing assumptions, etc.), understanding how models are used to simulate random phenomena, understanding how data are produced to estimate probabilities, recognizing how, when, and why existing inferential tools can be used, and being able to understand and utilize the context of a problem to plan and evaluate investigations and to draw conclusions. To read more about statistical thinking see Chance (2002).

Example of an item designed to measure statistical literacy:

A random sample of 30 first year students was selected at a public university to estimate the average score on a mathematics placement test that the state mandates for all freshmen. The average score for the sample was found to be 81.7 with a sample standard deviation of 11.45. Explain to someone who has not studied statistics what the standard deviation tells you about the variability of placement scores for this sample.

Example of an item designed to measure statistical reasoning:

The following stemplot displays the average annual snowfall amounts (in inches, with the stems being tens and leaves being ones) for a random sample of 25 American cities:

Without doing any calculations, would you expect the mean of the snowfall amounts to be larger, smaller, or about the same as the median? Why?

Example of an item designed to measure statistical thinking:

A random sample of 30 first year students was selected at a public university to estimate the average score on a mathematics placement test that the state mandates for all freshmen. The average score for the sample was found to be 81.7 with a sample standard deviation of 11.45.

A psychology professor at a state college has read the results of the university study. The professor wants to know if students at his college are similar to students at the university with respect to their mathematics placement exam scores. This professor collects information for all 53 first year students enrolled this semester in a large section (321 students) of his "Introduction to Psychology" course. Based on this sample, he calculates a 95% confidence interval for the average mathematics placement scores exam to be 69.47 to 75.72. Below are two possible conclusions that the psychology professor might draw. For each conclusion, state whether it is valid or invalid. Explain your choice for both statements. Note that it is possible that neither conclusion is valid.

1. The average mathematics placement exam score for first year students at the state college is lower than the average mathematics placement exam score of first year students at the university.
2. The average mathematics placement exam score for the 53 students in this section is lower than the average mathematics placement exam score of first year students at the university.