3. Test for Means, Variance and Proportions
1. Testing For Means
a. Testing hypothesis for a single population meanConsider Hypothesis testing about a population mean under three different conditions: | - When sampling is from a Normal Distributions with known variance.
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| - When sampling is from a Normal Distributions with unknown variance.
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| - When sampling is from a population that is not normally distributed.
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For a large sample size, when sampling is from normal distribution with knownvariance, the test hypothesis isFor example:
For a random sample of 5 persons, fed on a diet A, increased weight in pounds in a certain period were: 10, 12, 13, 11, 14 For another random sample of 7 persons, fed on a diet B, increased weight in pounds in a certain period were: 8, 9, 12, 14, 15, 10, 9 Test whether the diets A and B differ significantly as regards their effect on increase in weight at 5% level of significance. Solution:
n1 = 5, n2 = 7 X1 = 10, 12, 13, 11, 14 X2 = 8, 9, 12, 14, 15, 10, 9The calculated value is less than the tabulated value and hence the null hypothesis is accepted. The experiment provides no evidence against the hypothesis. Therefore, it is concluded that diets A and B do not differ significantly as regards their effect on increase in weight is concerned.2. Tests for Variances
a. Hypothesis Testing For a Single Population VarianceFor a given data available for analysis consisting of random samples drawn from a normally distributed population, the test hypothesis used for analysis of variance is
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