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1 Quantitative Variable
2 Quantitative Variables
- Least Squares Regression Line
Determine a Linear Model
Construct a linear model for the distribution of bivariate data (x,y).
Determine a Power or an Exponential Model
Construct a power model for the distribution of bivariate data (x,y) using the LSRL for (log x, log y). Construct an exponential model for the distribution of bivariate data (x,y) using the LSRL for (x, log y).
- Inference for Linear Regression
Construct a Confidence Interval for Slope Β
Construct a confidence interval for the slope Β of the least squares regression line.
Perform a Significance Test for Slope Β
Perform a significance test about the slope Β of the least squares regression line.
Normal, t, and χ2 Distributions
- Normal Distributions
- Normal Cumulative Density Function
Calculate the area under a Normal density curve.
- Inverse of the Normal Cumulative Density Function
Calculate the value corresponding to a given percentile in a Normal distribution.
- t Distributions
- t Cumulative Density Function
Calculate the area under a t density curve.
- Inverse of the t Cumulative Density Function
Calculate the value corresponding to a given area under a t density curve.
- χ2 Distributions
- χ2 Cumulative Density Function
Calculate the area under a χ2 density curve.
Studies and Experiments
Probability
- Basic Probability Rules
- P(A ⋃ B)
Calculate the probability of event A OR B using the general addition rule.
- P(A | B)
Calculate the probability of event A given that B has occurred using the conditional probability formula.
- Permutations and Combinations
- Permutations
Calculate the number of arrangements of size k out of a total number of n objects without replacement if ORDER MATTERS.
- Combinations
Calculate the number of arrangements of size k out of a total number of n objects without replacement if ORDER DOES NOT MATTER.
Random Variables
- Random Variables
- Discrete Random Variables
Calculate the mean and standard deviation of a discrete random variable X.
- Binomial and Geometric Distributions
- Binomial Distributions
Calculate the probability of a specific number of successes in a fixed number of independent trials and the same probablity of success on each trial.
- Geometric Distributions
Calculate the probability of the first success on a specified trial given the same probability of success on each trial.
Inference About Proportions
- Confidence Intervals
Construct a 1-Sample z Interval for p
Construct a confidence interval to estimate a population proportion.
Construct a 2-Sample z Interval for p1-p2
Construct a confidence interval to estimate the difference in proportions from two independent random samples (or groups).
- Significance Tests
Perform a 1-Sample z Test for p
Perform a significance test about a population proportion.
Perform a 2-Sample z Test for p1-p2
Perform a significance test about the difference in population proportions from two independent random samples (or groups).
Inference About Means
- Confidence Intervals
Construct a 1-Sample t Interval for μ
Construct a confidence interval to estimate a population mean.
Construct a 2-Sample t Interval for μ1 - μ2
Construct a confidence interval to estimate the difference between population means from two independent random samples (or groups).
- Significance Tests
Perform a 1-Sample t Test for μ
Perform a significance test about a population mean.
Perform a 2-Sample t Test for μ1 - μ2
Perform a significance test about the difference between population means from two independent random samples (or groups).
Inference About Categorical Data
- Significance Tests
Perform a Chi-Square Test for GOF
Perform a chi-square test for goodness of fit about a distribution of one categorical variable and answer the question: Does the distribution "fit" the claimed distribution in the population of interest?
Perform a Chi-Square Test for Homogeneity/Independence
Perform a chi-square test for homogeneity about the distribution of one categorical variables in two or more populations and answer the question: Are the distributions "homogenous" for several populations (or treatments)?
Perform a chi-square test for independence about the distributions of two categorical variables and answer the question: Are the two categorical variables "indepedent" (not associated)?