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8.19 Distribution of 't' for comparison of two samples Means Independent samples

Let x1i ( i = 1, 2, 3, ....., n1 ) and x2i ( i = 1, 2, 3, ....., n2 ) be two random independent samples drawn from two normal populations with mean m1 and m2 respectively but with same variance s2. Let and be sample means and let

Then the static t is given by

is called the pooled estimate of the population variance.

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Example Two types of drugs were used on 5 and 7 patients for reducing their weights in Jerry’s 'slim-beauty' health club. Drug A was allopathic and drug B was Herbal. The decrease in the weight after using drugs for six months was as follows :

Drug A :   10   12   13   11   14

Drug B :     8    9   12   14    15    10   9

Is there a significant difference in the efficiency of the two drug ? If not which drug should you buy ?

Solution:
Let the null hypothesis Ho : m1 = m2 or Ho : m1 - m2 = 0.

Alternative hypothesis Ha : m1 ¹ m2 or Ha : m1 - m2 ¹ 0

Thus the null hypothesis is accepted. Hence there is no significance in the efficiency of the two drugs. Since drug B is Herbal and there is no difference in efficiency between the two with no side effects, we should buy the Herbal drug.

Index

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