1.1 The definition of statistics; How to distinguish between a population and a sample and between a parameter and a statistic; How to distinguish between descriptive and inferential statistics
1.2 How to distinguish between qualitative data and quantitative data; How to classify data with respect to the four levels of measurements: nominal, ordinal, interval, and ratio
1.3 How to design a statistical study; How to collect data by taking a census, using a sampling, using a simulation, or performing an experiment; How to create a sample using random sampling, simple random sampling, stratified sampling, cluster sampling, and systematic sampling, and how to identify a biased sample
2.1 How to construct a frequency distribution including limits, boundaries, midpoints, relative frequencies, and cumulative frequencies; How to construct frequency histograms, frequency polygons, relative frequency histograms, and oglives
2.2 How to graph and interpret quantitative data sets using stem-and-leaf plots and dot plots; How to graph and interpret qualitative data sets using pie charts and Pareto charts; How to graph and interpret paired data sets using time series charts
2.3 Find the mean, median, and mode of a population and a sample; Find a weighted mean and the mean of a frequency distribution; Describe the shape of a distribution as symmetric, uniform, or skewed and compare the mean and median for each
2.4 Find the range of a data set; Find the variance and standard deviation of a population and or a sample; Use the Empirical Rule and Chebychev’s Theorem to interpret standard deviation; Approximate the sample standard deviation for grouped data
2.5 Find the first, second, and third quartiles of a data set; Find the interquartile range of a data set; Represent a data set graphically using a box-and-whisker plot; Interpret other fractiles such as percentiles; Find and interpret the standard score (z-score)
3.1 Identify the sample space of a probability experiment and identify simple events; Distinguish among classical probability, empirical probability, and subjective probability; Identify and use properties of probability
3.2 Find the probability of an event given that another event has occurred; Distinguish between independent and dependent events; Use the Multiplication Rule to find the probability of two events occurring in sequence; Use the Multiplication Rule to find conditional probabilities
3.3 Determine if two events are mutually exclusive; Use the Addition Rule to find the probability of two events
3.4 Use the Fundamental Counting Principle to find the number of ways two or more events can occur; Find the number of ways agroup of objects can be arranged in order; Find the number of ways to choose several objects from a group without regard to order; Use counting principles to find probabilities
4.1 Distinguish between discrete random variables and continuous random variables; Construct a discrete probability distribution and its graph; Determine if a distribution is a probability distribution; Find the mean, variance, and standard deviation of a discrete probability distribution; Find the expected value of a discrete probability distribution
4.2 Determine if a probability experiment is a binomial experiment; Find binomial probabilities using the binomial probability formula; Construct a binomial distribution and its graph; Find the mean, variance, and standard deviation of a binomial probability experiment
4.3 Find probabilities using the geometric distribution; Find probabilities using the Poisson distribution
5.1 Interpret graphs of normal probability distributions; Estimate areas under a normal curve and use them to estimate probabilities for random variables with normal distributions
5.2 Find the areas under standard normal curve
5.3 Find probabilities for normally distributed variables using a table and using technology
5.4 Find a z-score given the area under the normal curve; Transform a z-score to an x-value; Find a specific data value of a normal distribution given the probability
5.5 How to find sampling distributions and verify their properties; How to interpret the Central Limit Theorem; How to apply the Central Limit Theorem to find the probability of a sample mean
5.6 How to decide when the normal distribution can approximate the binomial distribution; How to find the correction for continuity; How to use the normal distribution to approximate binomial probabilities
6.1 How to find a point estimate and a maximum error of estimate; How to construct and interpret confidence intervals for the population mean; How to determine the required minimum sample size when estimating the population mean
6.2 How to interpret the t-distribution and use a t-distribution table; How to construct confidence intervals when n < 30 the population is normally distributed, and the standard deviation is unknown
6.3 How to find a point estimate for the population proportion; How to construct a confidence interval for a population proportion; How to determine the required minimum sample size when estimating a population proportion
6.4 How to interpret the chi-square distribution and use a chi-square distribution table; How to use the chi-square distribution to construct a confidence interval for the variance and standard deviation
7.1 A practical introduction to hypothesis tests; How to state a null hypothesis and an alternative hypothesis; How to identify type I and type II errors and interpret the level of significance; How to know whether to use a one-tailed or two-tailed statistical test and finding a P-value; How to make and interpret a decision based on the results of a statistical test; How to write a claim for a hypothesis test
7.2 How to find P-values and use them to test a mean; How to use P-values for a z-test; How to find critical values and rejection regions in a normal distribution; How to use rejection regions for a z-test
7.3 How to find critical values in a t-distribution; How to use the t-test to test a mean; How to use technology to find P-values and use them with a t-test to test a mean
7.4 How to use the z-test to test a population proportion p
7.5 How to find critical values for a chi-squared test; How to use the chi-squared test to test a variance or a standard deviation
8.1 An introduction to two-sample hypothesis testing for the difference between two population parameters; How to perform a two-sample z-test for the difference between two means using large independent samples
8.2 How to perform a t-test for the difference between two population means using small independent samples
8.3 How to decide whether two samples are independent or dependent; How to perform a t-test to test the mean of the difference for a population of paired data
8.4 How to perform a z-test for the difference between two population proportions
9.1 An introduction to linear correlation, independent and dependent variables, and the types of correlation; How to find a correlation coefficient; How to perform a hypothesis test for a population correlation coefficient
9.2 How to find the equation of a regression line; How to predict y-values using a regression line
9.3 How to interpret the three types of variation about a regression line; How to find and interpret the coefficient of determination; How to find and interpret the standard error of estimate for a regression line; How to construct and interpret a prediction interval for y
9.4 How to use technology to find a multiple regression equation, the standard error of estimate and the coefficient of determination; How to use a multiple regression equation to predict y-values
10.1 How to use the chi-square distribution to test whether a frequency distribution fits a claimed distribution
10.2 How to use a contingency table to find expected frequencies; How to use a chi-square distribution to test whether two variables are independent
10.3 How to interpret the F-distribution and use an F-table to find critical values; How to perform a two-sample F-test to compare two variances
10.4 How to use one-way analysis of variance to test claims involving three or more means; An introduction to two-way analysis of variance
11.1 How to use the sign test to test a population median; How to use the sign test to test the difference between two population medians (dependent samples)
11.2 How to use the Wilcoxon signed-rank test to determine if two dependent samples are selected from populations having the same distribution; How to use the Wilcoxon rank sum test to determine if two independent samples are selected from populations have the same distribution
11.3 How to use the Kruskal-Wallis test to determine whether three or more samples were selected from populations having the same distribution
11.4 How to use the Spearman rank correlation coefficient to determine whether the correlation between two variables is significant
