It is well known that the two-sample Student t test fails to maintain its significance level when the variances of treatment groups are unequal, and, at the same time, sample sizes are unequal. However, introductory textbooks in psychology and education often maintain that the test is robust to variance heterogeneity when sample sizes are equal.…

Stock car racing has seen tremendous growth in popularity in recent years. We introduce two datasets containing results from all Winston Cup races between 1975 and 2003, inclusive. Students can use any number of statistical methods and applications of basic probability on the data to answer a wide range of practical questions. Instructors and…

In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

Students in statistics service courses are frequently exposed to dogmatic approaches for evaluating the role of randomization in statistical designs, and inferential data analysis in experimental, observational and survey studies. In order to provide an overview for understanding the inference process, in this work some key statistical concepts in…

Item families, which are groups of related items, are becoming increasingly popular in complex educational assessments. For example, in automatic item generation (AIG) systems, a test may consist of multiple items generated from each of a number of item models. Item calibration or scoring for such an assessment requires fitting models that can…

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

This article describes the variety of strategies that can be used to determine the probability that a player wins a tennis game, given a probability of 60 percent that he or she wins each point. The article suggests strategies for using the problem in 9-12 classrooms.

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

In the discourse surrounding the Israeli-Palestinian conflict, extreme criticisms of Israel (e.g., Israel is an apartheid state, the Israel Defense Forces deliberately target Palestinian civilians), coupled with extreme policy proposals (e.g., boycott of Israeli academics and institutions, divest from companies doing business with Israel), have…

This paper describes a set of simulations which explore the way different features of lexical organisation affect the probability of finding a pair of associated words in a set of five randomly selected words. The simulation is equivalent to giving Ss a set of five words and asking if they can identify a pair of associated words among them. The…

Low-achieving students in many school districts are retained in a grade in order to allow them to gain the academic or social skills that teachers believe are necessary to succeed academically. This practice is highly controversial, with many researchers claiming that it leads to higher dropout rates although selection issues have complicated…

Purpose: This study determines the relationship between a medical school applicant's rural background and the likelihood of rural practice using different definitions of rural background. Methods: Cohort study of 599 physicians who entered the University of Virginia School of Medicine in 1990-1995 and graduated in 1994-1999. The…

Recent literature has focused on how school size influences both costs and outcomes (for example, test scores and educational attainment). It also emphasizes how school size may change the nature of educationally relevant social interactions among students, teachers, and administrators. However, there appears to be little corresponding evidence on…

In this paper an attempt is made to highlight some issues of interpretation of statistical concepts and interpretation of results as taught in undergraduate Business statistics courses. The use of modern technology in the class room is shown to have increased the efficiency and the ease of learning and teaching in statistics. The importance of…