Lottery numbers The fairness of the South African lottery was recently challenged by one of the countrys political parties. The lottery publishes historical statistics at its Website (http://www.nationallottery.co.za/lotto/ statistics.aspx). Here is a table of the number of times each of the 49 numbers has been drawn in the main lottery and as the bonus ball number as of June 2007: We wonder if all the numbers are equally likely to be the bonus ball. a) What kind of test should we perform? b) There are 655 bonus ball observations. What are the appropriate expected value(s) for the test? c) State the null and alternative hypotheses. d) How many degrees of freedom are there? e) The value of x2 is 34.5. Whats the P-value? f) State your conclusion.

Math 1070 – Elementary Statistics on the texts: Elementary Statistics with Excel, Third Custom Edition for Math1070; Georgia State University and Elementary Statistics; Eleventh Edition. Mario F. Triola, and coordinating PowerPoint Slides. Chapter 5 – Discrete Probability Distributions 5-3 – Binomial Probability Distributions Definition A binomial probability distribution results from a procedure that meets all of the following requirements: 1. The procedure has a fixed number of trials. 2. The trials must be independent. (the outcome of any individual trial does not affect the probability in the other trials.) 3. Each trial must have all outcomes classified into two categories (commonly referred to as