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8.14 Testing The Difference Between Means

denote the means of the samples drawn from the first and second population respectively, having means m1 and m2 and standard deviations s1 and s2 and if the sizes of the samples are n1 and n2, then it can be proved that the distribution of the difference between the means is normal with mean (m1 - m2 ) and S.D. is given by


Further, under the hypothesis Ho : m1 = m2 or Ho : m1 - m2 = 0 We see that

When the two samples belong to the same population, we have s1 = s2 = s then,

Similarly, the confidence limits for ( m1 - m2 ) at various levels of confidence are :

1)± 1.96 S at 95% level of confidence

2)± 2.58 S at 99% level of confidence

3)± 3. S at 99.73% level of confidence.

1. Note: Here S = S.E. =

For the samples drawn from the same population.

2. Note: If S.D. of two populations i.e. s1 , s2 are unknown, we use s.d. of samples in their places.


8.1 Population
8.2 Sample
8.3 Parameters and Statistic
8.4 Sampling Distribution
8.5 Sampling Error
8.6 Central Limit Theorem
8.7 Critical Region
8.8 Testing of Hypothesis
8.9 Errors in Tesitng of Hypothesis
8.10 Power o a Hypothesis Test
8.11 Sampling of Variables
8.12 Sampling of Attributes
8.13 Estimation
8.14 Testing the Difference Between Means
8.15 Test for Difference Between Proportions
8.16 Two Tailed and one Tailed Tests
8.17 Test of Significance for Small Samples
8.18 Students t-distribution
8.19 Distribution of 't' for Comparison of Two Samples Means Independent Samples
8.20 Testing Difference Between Mens of Two Samples Dependent Samples or Matched Paired Observations
8.21 Chi-Square
8.22 Sampling Theory of Correlation
8.23 Sampling Theory of Regression

Chapter 1

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