What is the null hypothesis and the alternative hypothesis? The records of an issue of the insurance company for damages, which in the past, customers had an average of 1.9 car accidents per day with a difference, 0036. The actuaries of the company's claim that the variance of the number of accidents per day is not greater than, 0036. Suppose we want to make a hypothesis test to see if there is support for the claim of Actuaries.
What is the null hypothesis and the alternative hypothesis that we would use for this test.
H0: σ ² = 0.0036 vs. H1: σ a‰ ² 0.0036
Hypothesis testing for population variance
Should we have a sample of a normal underlying distribution and variance σ ², so we can test the null hypothesis:
0: σ = ² m² σ0
for some ² σ0 fixed.
If H0 is true, then Îs ² = (n - 1) S ² / σ0 ². When Îs ² is the chi square with n - 1 degrees of freedom.
the other hypothesis, we have:
H1A: σ ²> σ0 ²
H1b: ² σ <² σ0
H1c: σ ² ² a‰ σ0
the test statistic is the same for all tests.
rejection regions for the above tests are as follows:
a) Îs ²> ² α Îs
b) Îs ² <α 1-Îs ²
c) Îs ² <Îs ² α / 2 or Îs ²> Îs ² 1-α / 2
Îs ² where α is the value such that:
P (Îs ²> Îs ² α) = α where Îs ² is the chi square with n - 1 degrees of freedom.
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H_o: variance = 0.0036
H_a: variance = / = 0.0036
Posted on February 16, 2010.
