1. Chi-squared goodnessof-fit test Visitors to an ecommerce website arrive at the site in one of four ways: by direct access (the visitor types the site's URL into a browser or clicks on a bookmark); via a link on another website, e-mail message, or banner ad: from a paid listing generated by a search engine; or via an organic [unpaid] listing generated by a search engine. Engine Ready, an Internet marketing company, randomly selected 2? U.S. e-commerce companies from its 500 clients and studied a total of 18.? million visits over a 2-year period. For each visit, data were collected on the trafc source and the size of the order placed by the visitor {in dollars). {If no order was placed, the order size is 0.} The relatiye frequency and average order size for each trafficsource type are shown in the following table. Trafc Source Relative Frequencyr Average Order {Dollars} Direct Access 0.20 5.69 Link 0.14 5.01 Paid Search Ad 0.41 1.91 Search Result 0.25 1.35 [Source Engine Ready, "Examining the Role Traffic Source Plays in Visitor Purchase Elehauiclr,\" 2008.] Suppose that Paws-n-Claws, an online pet-products retailer, conducts a test of the hypothesis that its trafc-source proportions are the same as the traffic-source proportions for the 18.? million website visits in the Engine Ready study. It selects a random sample of visits to its website and categorizes each visit according to the visits trafc source. The resulting category counts are shown in the following table. Traffic Source Observed Frequency Direct Access 50 Link 35 Paid Search Ad 72 Search Result 43 The expected frequency for the paid search ad category is The Paws-n-Claws statistician confirms that the expected frequencies for each of the four categories is 5 or more and proceeds to compute the chi- squared test statistic. Each of the four categories makes a contribution to the chi-squared test statistic. The contribution of the paid search ad category is The value of the test statistic is x= = Use the Distributions tool to help you answer the questions that follow.Chi-Square Distribution Degrees of Freedom = 6 O O 8 9 10 11 12 Use the rejection region method to perform the test for goodness of fit at a significance level of a = 0.05. According to the rejection region method, you: Reject Ho if x2 Using the rejection region method, the null hypothesis (that pi = 0.20, pz = 0.14, p= = 0.41, and p4 = 0.25) is The p-value is At a significance level of a = 0.05, using the p-value approach, the null hypothesis (that pi = 0.20, pz = 0.14, p= = 0.41, and p4 = 0.25 is Consider the average order size for the four traffic-source types from the Engine Ready study. A comparison of the observed and expected frequencies from the Paws-n-Claws study suggests that the average amount spent during a visit to the Paws-n-Claws website is the average amount spent during the visits covered by the Engine Ready study