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Example Two types of batteries are tested for their length of life and following results are obtained.

 No. of sample (n) Mean (x) Variance (s2) Battery A 10 500 hours 100 Battery B 10 560 hours 121

Is there a significant difference in the two batteries ?

Solution: The null hypothesis Ho : m1 = m2 or Ho : m1 - m2 ¹ 0

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

i.e. there is no significant difference in the two batteries.

The degree of freedom n (df) = 10 + 10 - 2 = 18

For n = 18, t0.05 = 2.1

Therefore, 12.2 > 2.1 ( much higher )

Thus the difference is highly significant ( rejection of Ho )

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Example To test the effect of a fertilizer on rice production, 24 equal plots of a certain land are selected. Half of them were treated with fertilizer leaving the rest untreated. Other conditions were the same. The mean production of rice on untreated plots was 4.8 quintals with standard deviation of 0.4 quintal, while the mean yield on the treated plots was 5.1 quintals with a standard deviation of 0.36 quintal. Can we say that there is significant improvement in the production of rice due to use of fertilizer at 0.05 level of significance ?

Solution: The null hypothesis Ho : m1 = m2 or Ho : m1 - m2 = 0

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

or Ha : m1 > m2 and the fertilizer improved the yield.

For n (df) = 12 + 12 - 2 = 22, t0.05 = 2.07

Therefore, 1.44 < 2.07

Thus we accept Ho i.e. there is no significant difference in rice production due to the use of fertilizer.

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