What is the null hypothesis and alternative hypothesis?

The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of .0036. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to .0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim.


What is the null hypothesis and the alternative hypothesis that we would use for this test.|||H0: 蟽虏 = 0.0036 vs. H1: 蟽虏 鈮?0.0036











Hypothesis Test for population variance





If we have a sample from an underlying normal distribution and variance 蟽虏 then we can test the null hypothesis:





H0: 蟽虏 = 蟽0虏


for some fixed 蟽0虏.





If H0 is true then 围虏 = (n - 1) S虏 / 蟽0虏. Where 围虏 is the chi square with n - 1 degrees of freedom.





for the alternate hypothesis we have:





H1a: 蟽虏 %26gt; 蟽0虏


H1b: 蟽虏 %26lt; 蟽0虏


H1c: 蟽虏 鈮?蟽0虏





the test statistic is the same for all tests.





the rejection regions for the above tests are:


a) 围虏 %26gt; 围虏伪


b) 围虏 %26lt; 围虏1-伪


c) 围虏 %26lt; 围虏伪/2 or 围虏 %26gt; 围虏1-伪/2





where 围虏伪 is the value such that:


P(围虏 %26gt; 围虏伪) = 伪 where 围虏 is the chi square with n - 1 degrees of freedom.





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http://people.richland.edu/james/lecture鈥?/a>|||H_o : variance = 0.0036


H_a: variance =/= 0.0036