Sampling Distr of Sampling Distr of

For Finite Populationi.e. nn//NN << .05 .05

For Infinite Population

Interval Estimation known unknown n > 30

n < 30 (Pop. Normally distr.)

Margin of error:

Interval estimation of a population proportion:

Margin of error:

Sample Size for a Hypothesis Test about a Population Mean

Properties of the Sampling Distribution of Expected Value: Standard Deviation:

Large Sample case: ( n 1 >=30 and n 2 >=30) Interval Estimate with 1 and 2 Known:

Interval Estimate with 1 and 2 Unknown: , where:

Small sample case: ( n 1 < 30 and/or n 2 < 30)

Interval Estimate with 2 known: , where

Interval Estimate with 2 Unknown:

Where ,

Properties of Sampling Distribution of

Expected Value: Standard Deviation:

Interval Estimate:

Point Estimator of :

Test statistic

Point Estimator of when p1 = p2 ,

Test Statistic for goodness of fit: with degrees of freedom = k-1 & all

Expected freq. for contingency Tables (assuming independence):

Test statistic for independence: (deg. of freedom = (n-1)(m-1)& all

Between samples estimate of popln variance- Mean Square Between:

MSB = Sum of Squares Between (SSB) Degrees of freedom of SSB = k-1

Within samples estimate of popln variance- Mean Square within:

MSW = Sum of Squares due to error (SSE) Degrees of freedom of SSE = nt-k

Test statistic for equality of k population means: F = MSB / MSE

ANOVA TABLESource of Sum of Degrees of Mean where, Variation Squares Freedom Squares FTreatment SSB k - 1 MSB MSB/MSE = SSB + SSWError SSE nT - k MSE and SST / (nT – 1) is overall Total SST nT – 1 sample variance of nT obs.

Fisher’s LSD Procedure Test Statistic: (nT – k degrees of freedom)

Fisher’s LSD procedure based on test statistic rejects H0 : μi = μj when

Simple Linear Regression Model y = 0 + 1x + Simple Linear Regression Equation E(y) = 0 + 1xEstimated Simple Linear Regression Equation y = b0 + b1xLeast Squares Criterion Slope for the Estimated Regression Equation

SST = SSR + SSE

Coefficient of Determination: r2 = SSR/SSTWhere: SST = total sum of squares, SSR = sum of squares due to regression

SSE = sum of squares due to errorSample Correlation Coefficient: An Estimate of s2 = MSE = SSE/(n-2)where: Hypotheses H0: 1 = 0 Ha: 1 = 0

Test Statistic where

Rejection Rule: Reject H0 if t < -t/ or t > t/ (n - 2 degrees of freedom)

Confidence Interval for 1:

Confidence Interval Estimate of E(yp) where

Prediction Interval Estimate of yp yp + t/2 sind (n - 2 degrees of freedom)

Where

Residual for Observation I:

Standardized Residual for Observation I:

Where