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Thus there is no reason to reject Ho. To find the limits,

Example Ten individuals are chosen at random from the population and their heights are found to be inches 63, 63, 64, 65, 66, 69, 69, 70, 70, 71. Discuss the suggestion that the mean height in the universe is 65 inches given that for 9 degree of freedom the value of studentís 't' at 0.05 level of significance is 2.262.

Solution: xi = 63, 63, 64, 65, 66, 69, 69, 70, 70, 71 and
n = 10

The difference is not significant at a t 0.05 level thus Ho is accepted and we conclude that the mean height is 65 inches.

Example Nine items of a sample have the following values 45, 47, 50, 52, 8, 47, 49, 53, 51, 50. Does the mean of the 9 items differ significantly from the assumed population mean of 47.5 ?

Given that for degree of freedom = 8. P = 0.945 for t = 1.8 and P = 0.953 for t = 1.9.

Solution: Given that for degree of freedom = 8. P = 0.945 for t = 1.8 and P = 0.953 for t = 1.9.

\ S xi = 45 + 47 + 52 + 48 + 47 + 49 + 53 + 51 + 50 = 442

n = 9

Therefore for difference of t = 0.043, the difference of P = 0.0034. Hence for t = 1.843, P = 0.9484. Therefore the probability of getting a value of t > 1.43 is ( 1 - 0.9484 ) = 0.051 which is in fact 2 ī 0.051 = 0.102 and it is greater than 0.05. Thus Ho is accepted, i.e. the mean of 9 items differ significantly from the assumed population mean.


Example A certain stimulus administered to each of 12 patients resulted in the following increments in 'Blood pressure' 5, 2, 8, -1, 3, 0, 6, -2, 1, 5, 0, 4. Can it be concluded that the stimulus will in general be accompanied by an increase in blood pressure, given that for all df the value of t0.05 = 2.201?

Solution:

The null hypothesis Ho : m = 0 i.e. assuming that the stimulus will not be accompanied by an increase in blood pressure (or the mean increase in blood pressure for the population is zero).

Now

The table value, t0.05, n = 11 = 2.201

Therefore, 2.924 > 2.201

Thus the null hypothesis Ho is rejected i.e. we find that our assumption is wrong and we say that as a result of the stimulus the blood pressure will increase.

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





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