# Examples of Testing Conjectures

• Reasoning About Center and Spread: How do Students Spend Their Time? This activity builds upon the ideas of distribution; shape, center and spread. The lesson begins by having students predict which daily activities will have a lot and which activities will have a little variation. The activity then has the students examine their choices through the use of computer software. The final task in the activity has the students use reasoning about distributions to examine graphs and summary statistics to choose variables that have a lot and have a little variability.
• Seeing and Describing the Predictable Pattern: The Central Limit Theorem This activity is designed to develop student understanding of how sampling distributions behave by having them make and test conjectures about distributions of means from different random samples; from three different theoretical populations (normal, skewed, and multimodal). Students investigate the impact of sample size and population shape on the shape of the sampling distribution, and learn to distinguish between sample size and number of samples. Students then apply the Empirical Rule (when appropriate) to estimate the probability of sample means occurring in a specific interval.
• Using Your Hair to Understand Descriptive Statistics: The purpose of this activity is to enhance students' understanding of various descriptive measures in statistics. In particular, students will gain a visual and hands-on understanding of means, medians, quartiles, and boxplots without doing any computations by completing this activity.
• A ducks story- introducing the idea of testing (statistical) hypotheses: By means of a simple story and a worksheet with questions we pose to the students we guide them from research question to arriving to a conclusion. The whole process is simply reasoning, no formulas. However we use the reasoning already done by the student to introduce the standard vocabulary of testing statistical hypotheses (null & alternative hypotheses, p-value, type I and type II error).
• An In-Class Experiment to Estimate Binomial Probabilities: This hands-on activity is appropriate for a lab or discussion section for an introductory statistics class, with 8 to 40 students. Each student performs a binomial experiment and computes a confidence interval for the true binomial probability. Teams of four students combine their results into one confidence interval, then the entire class combines results into one confidence interval. Results are displayed graphically on an overhead transparency, much like confidence intervals would be displayed in a meta-analysis. Results are discussed and generalized to larger issues about estimating binomial proportions/probabilities.
• Independent Samples t-Test: Chips Ahoy??? vs. Supermarket Brand: In this hands-on activity, students count the number of chips in cookies in order to carry out an independent samples t-test to see if Chips Ahoy??? cookies have a higher, lower, or different mean number of chips per cookie than a supermarket brand.