Small Sampling Theory Presentation1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Introduction

t - Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Properties of t-Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Steps involved in testing of hypothesis. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Applications of t - distribution ,[object Object],[object Object],[object Object],[object Object]

1. Test of Hypothesis about the population mean( σ unknown and small sample size ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Test of hypothesis about the difference between two means ,[object Object],[object Object],[object Object],[object Object]

(a) Case of equal variances ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

(b) Case of unequal variances ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confidence interval for the difference between two means Two samples of sizes n 1 and n 2 are randomly and independently drawn from two normally distributed populations with unknowns but equal variances. The 100(1- α )% confidence interval for µ 1 - µ 2 is given by:

(3) Test of hypothesis about the difference between two means with dependent samples (paired t-test) ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

(4) Testing of hypothesis about coefficient of correlation. ,[object Object],[object Object],[object Object]

Case 1: testing the hypothesis when the population coefficient of correlation equals zero, i.e., H o : ρ =0 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Case 2: testing the hypothesis when the population coefficient of correlation equals some other value than zero, i.e., H o : ρ = ρ o ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object]

Case 3: testing the hypothesis for the difference between two independent correlation coefficients ,[object Object],[object Object],[object Object]

The F - Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Probability density function ,[object Object]

Properties of F-distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Testing of hypothesis for equality of two variances ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confidence interval for the ratio of two variances ,[object Object],[object Object],[object Object]

Small Sampling Theory Presentation1

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Small Sampling Theory Presentation1