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Chi Square Statistic Test Definition
Chi Square Statistic Test which is defined as chi-square test or test is any statistical hypothesis test that is commonly used to compare observed data with the data that is expected to obtain according to a specific hypothesis. It is the Chi-squared distribution when the null hypothesis is true or any in which this is asymptotically true. The meaning of the sampling distribution is that if the null hypothesis is true it can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.
If a sample of size n is taken from a population having a normal distribution then there is a well-known result such as variance which allows a test to be made of whether the variance of the population has a predetermined value.
For example: a manufacturing process is in a stable condition for a long period there by allowing a value for the variance to be determined essentially without error and suppose that a variant of the process is being tested giving rise to a small sample of product items whose variation is to be tested. The test statistic T in this case could be set to be the sum of squares about the sample mean which is divided by the nominal value for the variance which is the value to be tested as holding and then T has a chi-squared distribution with n − 1 degrees of freedom.
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What is the chi square test?
Chi Square Statistic Test is the test where the variance of a normally distributed population has a given value based on a sample variance and such a test is uncommon in practice because the values of variances are to test against are seldom known exactly. The chi-square test statistic is an overall measure of how close the observed frequencies are to the expected frequencies and which has the following form
The null hypothesis of independence is rejected if is large. This is because this means that observed frequencies as well as expected frequencies are far apart and the chi-square curve is used to judge whether the calculated test statistic is large enough. H0 is rejected if the test statistic is large.
