Number of Ads Clicked 0 2 Number of Users 368 233 69 13 Web Hits We can use this Chi-Squared test of Goodness of Fit to test whether the observed counts match a particular distribution. Managers of the Web site plan to use a Poisson model to summarize how often users click on ads. If it fits well, they will use this model to summarize concisely the volume of traffic headed to advertisers and to measure the effects of changes in the Web site on traffic patterns. Data were collected on a sample of 685 users that visited the Web site during a recent weekday evening. We use the Chi-Squared test to test the null hypothesis that a Poisson model describes the number of ads clicked by a user well (good fit of the data). Which condition of the Chi-Squared test is not met? How can we fix it? We use a Poisson random variable to describe counts of data. It is appropriate for situations like The number of calls arriving at the help desk in a 10-minute interval .The number of imperfections per square meter of glass panel Poisson Random Variable 1. Describes the number of events determined by a random process during an interval of time or space 2. Is not finite (possible values are infinite) 3. Is defined by & (lambda), the rate of events The Poisson Probability Distribution E(X) = 1, Var(X) = 2 Calculate the Poisson probability for the number of ads clicked in the table above and also the expected number of ads clicked. How can we address the violation of the sample size condition for the Chi-Squared test? What is the Chi-Squared test statistic? What is the degree of freedom? What is the corresponding p-value? Is the distribution of the number of ads clicked by users consistent with a Poisson distribution? Can managers of the website use this model to summarize user behavior? (see calculation in Web hits)