Counting Rule for Combinations



Sample Mean

[pic]

Population Mean

[pic]

Interquartile Range

[pic]

|Sample Variance |Sample Standard Deviation |

|[pic] |[pic] |

|Population Variance |Population Standard Deviation |

|[pic] |[pic] |

|Coefficient of Variation | |

|[pic] | |

Z-Score

[pic] or [pic]

|Sample Covariance |Population Covariance |

|[pic] |[pic] |

|Pearson Product Moment Correlation Coefficient (Pearson R): |

|Sample Data |Population Data |

|[pic] |[pic] |

Weighted Mean

[pic]

|Sample Mean for Grouped Data |Population Mean for Grouped Data |

|[pic] |[pic] |

|Sample Variance for Grouped Data |Population Variance for Grouped Data |

|[pic] |[pic] |

|Sample Standard Deviation for Grouped Data |Population Standard Deviation for Grouped Data |

|[pic] |[pic] |

Counting Rule for Combinations

[pic]

Counting Rule for Permutations

[pic]

Computing Probability Using the Complement

[pic]

Addition Law

[pic]

Conditional Probability

[pic] or [pic]

Multiplication Law

[pic] or [pic]

Multiplication Law for Independent Events

[pic]

Expected Value of a Discrete Random Variable

[pic]

Variance of a Discrete Random Variable

[pic]

Binomial Probability Function

[pic]

Expected Value and Variance for the Binomial Distribution

[pic] [pic]

Poisson Probability Function

[pic] where [pic] = the probability of x occurrences in an interval

[pic] = the expected value or mean number of occurrences in an interval

e = 2.718

Sampling & Sampling Distributions

| |

|Standard Deviation of [pic] (Standard Error) |

|For a Finite Population |For an Infinite Population |

|[pic] |[pic] |

Sampling Proportions

| |

|Standard Deviation of [pic] (Standard Error) |

|For a Finite Population |For an Infinite Population |

|[pic] |[pic] |

Interval Estimate of a Population Mean: [pic] Known

[pic] Where [pic]

Interval Estimate of a Population Mean: [pic] Unknown

[pic] Where [pic]

Sample Size for an Interval Estimate of a Population Mean

[pic]

Interval Estimate of a Population Proportion

[pic]

Sample Size for an Interval Estimate of a Population Proportion

[pic]

Sampling Proportions

Test Statistic for Hypothesis Tests About a Population Proportion

[pic]

| |

|Standard Deviation of [pic] (Standard Error) |

|For a Finite Population |For an Infinite Population |

|[pic] |[pic] |

Interval Estimate of a Population Mean: [pic] Known

[pic] Where [pic] [pic]

Interval Estimate of a Population Mean: [pic] Unknown

[pic] Where [pic] [pic]

Interval Estimate of a Population Proportion

[pic]

Interval Estimate of the Difference Between Two Population Proportions

[pic]

Sample Size for an Interval Estimate of Population Proportions and Normal Distributions

[pic] [pic]

Z-Value Formulas for Normal and “Approximately Normal” Distributions – Calculations of Test Statistics

[pic] [pic] [pic][pic]

Test Statistic for Hypothesis Tests About Two Independent Proportions

[pic]

Standard Error of [pic]

[pic]

Degrees of Freedom for the t Distribution Using Two Independent Random Samples

[pic]

Test Statistic for Hypothesis Tests About Two Independent Means; Population Standard Deviations Unknown

[pic]

Test Statistic for Hypothesis Tests Involving Matched Samples

[pic]

Mean Difference Involving Matched (or Dependent) Samples

[pic]

Standard Deviation Notation Used for Matched Samples

[pic]

Interval Estimate of Means of Matched Samples

[pic]

Test Statistic for Hypothesis Tests About a Population Variance

[pic] [pic]

Test Statistic for Hypothesis Tests About Two Population Variances when [pic]

[pic] [pic] and [pic]

Interval Estimate of the Difference Between Two Population Means: σ1 and σ2 Known and Unknown

[pic] (σ known) [pic] (σ unknown)

Pooled Sample Standard Deviation (Assumptions that σ1 and σ2 are equal and populations are approximately normal) & Test Statistic for Comparison of Independent Samples

[pic] [pic] [pic] [pic]

Chi-Square Goodness of Fit Test Statistic

[pic]

Chi-Square Test for Independence Test Statistic

[pic]

Testing for the Equality of k Population Means—ANOVA

Sample Mean for Treatment j

[pic]

Sample Variance for Treatment j

[pic]

Overall Sample Mean (Grand Mean)

[pic]

Mean Square Due to Treatments

[pic]

Sum of Squares Due to Treatments

[pic]

Mean Square Due to Error

Sum of Squares Due to Error

[pic]

Test Statistic for the Equality of k Population Means

[pic]

Total Sum of Squares

[pic]

Partitioning of Sum of Squares

[pic]

Multiple Comparison Procedures

Test Statistic for Fisher’s LSD Procedure

[pic]

Fisher’s LSD

[pic]

Completely Randomized Designs

Mean Square Due to Treatments

[pic]

Mean Square Due to Error

[pic]

F Test Statistic

[pic]

Randomized Block Designs

Total Sum of Squares

[pic]

Sum of Squares Due to Treatments

[pic]

Sum of Squares Due to Blocks

[pic]

Sum of Squares Due to Error

[pic]

Factorial Experiments

Total Sum of Squares

[pic]

Sum of Squares for Factor A

[pic]

Sum of Squares for Factor B

[pic]

Sum of Squares for Interaction

[pic]

Sum of Squares for Error

[pic]

Simple Linear Regression Formulas

Simple Linear Regression Model

[pic]

Simple Linear Regression Equation

[pic]

Estimated Simple Linear Regression Equation

[pic]

Least Squares Criterion

[pic]

Slope and y-Intercept for the Estimated Regression Equation

[pic]

[pic]

Total Sum of Squares

[pic]

Sum of Squares Due to Error

[pic]

Sum of Squares Due to Regression

[pic]

Total Sum of Squares for Regression

[pic]

Coefficient of Determination

[pic]

Sample Correlation Coefficient

[pic]

Mean Square Error (Estimate of σ2 )

[pic]

Standard Error of the Estimate

[pic]

Standard Deviation of b1

[pic]

Estimated Standard Deviation of b1

[pic]

t Test Statistic

[pic]

Mean Square Regression

[pic]

F Test Statistic

[pic]

Estimated Standard Deviation of [pic]

[pic]

Confidence Interval for [pic]

[pic]

Estimated Standard Deviation of an Individual Value

[pic]

Prediction Interval for yp

[pic]

Residual for Observation i

[pic]

Standard Deviation of the i th Residual

[pic]

Standardized Residual for Observation i

[pic]

Leverage of Observation i

[pic]

Nonparametric Method Formulas

Mann-Whitney-Wilcoxon Test (Large Sample)

[pic]

[pic][pic]

Kruskall-Wallis Test Statistic

[pic]

Spearman Rank –Correlation Coefficient

[pic]

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[pic]

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