1. Goodness-of-fit tests Multinomial population Aa Aaa Visitors to an e-commerce
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Question
1. Goodness-of-fit tests Multinomial population Aa Aaa Visitors to an e-commerce 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 27 US. e-commerce companies from its 500 clients and studied a total of 18.7 million visits over a 2-year period. For each visit, data were collected on the traffic source and the size of the order placed by the visitor (in dollars). (If no order was placed, the order size is 0.) The relative frequency and average order size for each traffic source type are shown in the following table. Traffic Source Average order (Dollars) Relative Frequency irect Access 0.20 5.69 0.14 Link 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 Behavior," 2008.] Suppose that SparkleMotion, an online jewelry retailer, conducts a test of the hypothesis that its traffic-source proportions are the same as the traffic-source proportions for the 18.7 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 visit's traffic source. The resulting category counts are shown in the following table. Traffic Source Observed Frequency Direct Access 31 Link 18 93 Paid Search Ad 58 Search Result The expected frequency for the link category is The SparkleMotion statistician confirms that the expected frequencies for each of the four categories is 5 or more and proceeds to compute the chi square test statistic. Each of the four categories makes a contribution to the chi-square test statistic. The contribution of the link category is The value of the test statistic is x2 Use the Distributions tool to help you answer the questions that follow.Explanation / Answer
here
expected frequency of link =28
contributio o flink=3.57
value of X2 =8.35
reject Ho if X2 >=6.2514
rejected
p value=0.0393
not equal
observed Expected Chi square year P O E=total*p =(O-E)^2/E direct 0.200 31 40 2.03 link 0.140 18 28 3.57 paid search 0.410 93 82 1.48 search result 0.250 58 50 1.28 200 200 8.35Related Questions
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