Therefore, the chi-square distribution has one parameter: k – a positive integer that specifies the number of degrees of freedom.
As mentioned previously, the chi-square distribution is mainly used in hypothesis testing. Unlike more recognized distributions, as the normal distribution and the exponential distribution, the chi-square distribution is rarely used to model natural phenomena. It arises in the following hypothesis tests, among other.
The main reason that the chi-square distribution is widely used in hypothesis testing is its association with the normal distribution.. Many hypothesis tests use a test statistic, as the t statistics in a test t. For these hypothesis tests, as the sample size, North, increases, the sampling distribution of the test statistic approximates the normal distribution (Central limit theorem). Since the test statistic (What t) it has an asymptotically normal distribution, provided the sample size is large enough, the distribution used for the hypothesis test can be approximated through a normal distribution. Testing hypotheses using a normal distribution is well understood and relatively easy. The simplest chi-square distribution is the square of a standard normal distribution. Then, provided that a normal distribution can be used for a hypothesis test, a chi square distribution could be used.
A chi-square distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom, etc.
The CHIINV The function returns the inverse of the right-tailed probability of the chi-square distribution. And probability = CHIDIST (x, …), after CHIINV (probability, …) = x. This function can be used to compare the observed results with the expected ones in order to choose if your original hypothesis is valid..