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Example A stenographer claims that she can take dictation at the rate of 120 words per minute. Can we reject her claim on the basis of 100 trials in which she demonstrated a mean of 116 words with standard deviation of 15 words ?

Solution: The hypothesis to be tested is that her claims to be accepted.

In notations Ho : m = 120 and Ha : m ¹ 120

Substituting, = 116, s = 15, n = 100 in

The difference is not significant at both 5% and 1% level of significance i.e. the value of z - score 2.67 is highly significant. Hence Ho is rejected i.e. her claim is to be rejected.

If somebody is interested in the number of trials on the basis of which, with the same figure, her claim would not have been rejected, he can proceed as

i.e. n = 54 trials.

Example An automatic machine was designed to pack exactly 2 kg. of tea. A sample of 100 packs was examined to test the machine. The average weight was found to be 1.94 kg. with standard deviation of 0.10 kg. is the machine working properly ?

Solution:The null hypothesis to be tested is that the machine is working properly.

In notations Ho : m = 2 kg. and Ha : m ¹ 2kg.

Substituting, = 1.94, s = 0.10 , n = 100 in

The z-score is highly significant, hence, we reject Ho on the basis of this sample i.e. the machine is not working properly.


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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