Goodness of fit binomial distribution example
May 17, 2013 I work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the nullI work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the null hypothesis, and one where it is estimated from the data. goodness of fit binomial distribution example
Example Consider a binomial random variable Y with mean (expected value) np and variance y 2 np(1p). From the Central Limit Theorem, we know that Z (Ynp) y has an approximately Normal(0, 1) distribution for large values of n. Then Z is approximately (1), since the square of a normal random variable has a chisquare distribution.
GoodnessofFit Test The 2 goodnessoffit test use the chisquare statistic (based upon the chissquare distribution) to compare frequency data to a model stated by the null hypothesis. Continuing with our example: H 0: The probability of birth is the same every day of the week. H A: The probability of birth is not the same every day of the week. The resulting value can be compared with a chisquared distribution to determine the goodness of fit. (including location and scale parameters and shape parameters) for the distribution plus one. For example, for a 3parameter Weibull distribution, Binomial case A binomial experiment is a sequence of independent trials ingoodness of fit binomial distribution example Chisquared goodnessoffit test whether the data follows binomial distribution. up vote 1 down vote favorite. 1. The number of boys in 500 families with 5 children is investigated. There were 20 families with no boy, 75 with 1, 145 with 2, 140 with 3, 85 with 4, and 35 with 5 boys.