Mathematics - MATH 122

Course Description

This course includes an introduction to statistics, statistical descriptions, frequency distributions, possibilities and probabilities, probability distributions, sampling and sampling distributions, testing hypotheses based on measurements, count data, paired data and use of nonparametric tests.

Prerequisites

(A requirement that must be completed before taking this course.)

Course Competencies

Upon successful completion of the course, the student should be able to:

• Create visual presentations using sample data both by hand and by using statistical software, including a tabular frequency distribution, stem-and-leaf plot, histogram, frequency polygon and pie chart.
• Compute descriptive statistics both by using an algorithm and by using statistical software, including the mean, median, mode, fractiles, range, variance and standard deviation.
• Determine whether a given sampling method yields a random sample, simple random sample, stratified sample, etc.
• Use a random number generator to select a random sample from a given population.
• Determine the number of possible outcomes of an event with the aid of the addition, multiplication, complement, factorial and other rules.
• Calculate probability of an event by using the classical approach.
• Estimate the probability of an event by using the relative frequency approach.
• Determine the conditional probability of one event given another event by using the defining formula for conditional probability.
• Determine probabilities for various discrete distributions (including the uniform, binomial and hypergeometric) by all of the following means: a formula, a table and statistical software.
• Determine probabilities for various continuous distributions (including the Gaussian normal and Student's t) by using a formula and either a table or statistical software.
• Interpret probabilities of a discrete random variable as the area of bars in its histogram.
• Interpret probabilities of a continuous random variable as the area under the graph of its density function.
• Solve practical problems involving probability distributions.
• Determine the mean (expected) value and the standard deviation of a discrete random variable using its probability distribution.
• Determine whether two events are independent of one another by using their probabilities.
• Determine a confidence interval for a population mean, based on a random sample and the normal or t-distribution (as appropriate), both by using a formula and table and by using statistical software.
• Test a hypothesis regarding one, two or several population means, based on random sample(s) and the normal, t- or ANOVA distribution (as appropriate), both by using a formula and table and by using statistical software.
• Determine a confidence interval for a population proportion, based on a random sample and the normal distribution, both by using a formula and table and by using statistical software.
• Test a hypothesis regarding one, two or several population proportions, based on a random sample(s) and the normal, t or chi-squared distribution (as appropriate), both by using a formula and table and by using statistical software.
• Determine Pearson's linear correlation coefficient r for a sample of bivariate data, both by using a formula and by using statistical software.
• Determine the least-squares linear regression fit to a sample bivariate data.
• Test a hypothesis regarding the linear correlation between two variables, based on a random sample and on critical values of the r-distribution, both with the aid of a table and the aid of statistical software.
• Test a hypothesis regarding one or two population medians or a population proportion, based on a random sample(s) and the sign test.
• Test a hypothesis regarding the linear correlation between two variables, based on a random sample and Spearman's rank-correlation test.
• Investigate sampling distributions of statistics.

Course Schedule