# Quantitative Analysis and Decision Methods Formulas

**Topics:**Normal distribution, Variance, Standard deviation

**Pages:**7 (853 words)

**Published:**November 22, 2011

MISCELLANEOUS, COMMONLY USED FORMULAS

Finite population correction factor:

Multiply SE of sample mean by fpc to make the correction

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Independent samples of same population with same standard deviation (variances are equal). Confidence interval:

df for t-multiple is (df1 + df2), or (n1 – 1) + (n2 - 1)

Pooled estimate of common standard deviation:

SE of difference between two sample means

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Confidence interval for differences in sample means when variance is not equal.

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df for t-multiple is given by complex formula not shown in book when variance is not equal. Use StatTools.

Confidence interval for difference between two proportions.

SE for difference between two proportions.

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Chapters 2 and 3 Describing the Distribution of a Single Variable and Finding Relationships among variables

Mean Formula

Excel Function: = AVERAGE

Coefficient of Variation: Standard Deviation / Mean

Standard Deviation: square root of variance

Sample Variance

Population Variance

Excel Function: Variance = VAR

Standard Deviation = STDEV

Mean Absolute Deviation

Covariance

Correlation

Excel Function: =CORREL

Chapter 4: Probability and Probability Distributions

Conditional probability:

P(A|B) = P(A and B) / P(B)

Multiplication rule:

P(A and B) = P(A|B) P(B)

If two events are INDEPENDENT:

P(A and B) = P(A) P(B)

Variance of a Probability Distribution:

Standard Deviation of a Probability Distribution:

Conditional Mean:

* when the mean of a variable depend on an external event

Covariance between X and Y:

Correlation between X and Y:

Joint Probability Formula:

P(X = x and Y = y) = P(X = x|Y = y) P(Y = y)

Alternative formula:

P(X = x and Y = y) = P(Y = y|X = x) P(X = x)

Joint probability formula for independent random variables:

P(X = x and Y = y) = P(X = x) P(Y = y)

Expected value of a weighted sum of random variables:

E(Y) = a1E(X1) + a2E(X2) + … + anE(Xn)

Chapter 5 Normal, Binomial, Poisson, and Exponential Distributions

Normal Density Function

Mean

Stdev

Chapter 7 Sampling and Sampling Distributions

Unbiased Property of Sample Mean

Standard Error of Sample Mean

Approximate Standard Error of Sample Mean

(Approximate) Confidence Interval for Population Mean

Standard Error of Mean with Finite Population Correction Factor

Finite Population Correction Factor

Chapter 8 Confidence Interval Estimation

Typical Form of Confidence Interval

Standardized Z-Value

Standardized Value

Confidence Interval for Population Mean

Point Estimate for Population Total

Mean and Standard Error of Point Estimate for Population Total

Approximate Standard Error of Point Estimate for Population Total

Standard Error of Sample Proportion

Confidence Interval for a Proportion

Upper Limit of a One-Sided Confidence Interval for a Proportion

Confidence Interval for Difference Between Means

Standard Error of Difference Between Sample Means

Confidence Interval for Difference Between Proportions

Standard Error of Difference Between Sample Proportions

Sample Size Formula for Estimating a Mean

Sample Size Formula for Estimating a Proportion

Sample Size Formula for Estimating the Difference Between Means

Sample Size Formula for Estimating the Difference Between Proportions

Chapter 9 Hypothesis Testing

Hypothesis Test for a Population Mean: one-sample t-test

P(t-value>const)= α.

Excel functions: TDIST() and TINV()

Test statistic for test of proportion:

Test statistic for paired samples test of differences between means:...

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