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Use c2 test to assess the correctness of the hypothesis that the digits were distributed in an equal manner in the tables from which they are chosen.

Solution: Our hypothesis is that the digit were distributed equally in the tables as correct. The expected frequencies of the digits would be :

The numbers of degree of freedom r (df) = ( c - 1 ) ( r - 1 )

                = ( 10 - 1 ) ( 2 - 1 )

                = 9

From the table, c20.03, n = 9 = 16.919

Therefore, 4.3 < 16.919

Thus calculated value of   c2  is less than table value of

c20.05, n = 9. Hence our hypothesis is correct.

Example In a certain town 100 persons were randomly chosen and interviewed for their educational stature. The results are as

Can you say that education depends on the sex of the individual?

Solution: The null hypothesis : That there is no association between education and sex. On this hypothesis the expected frequencies are as below :

From the table c20.05, n = 2 = 5.99 and c2 0.01, n = 2 = 9.21

Thus the calculated value of c2 is highly significant and the null hypothesis which stated that, education does not depend on sex is, discredited.


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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