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The table lists the number of games played from 4 to 7 in the Major League Baseball championship the World Series over the last 100 years It also includes the expected proportions for the number of games played with teams of equal abilities Games Played Actual Contests Expected Proportion 4 18 2 16 b Which is the alternative hypothesis 5 22 4 16 6 21 5 16 Use a 0 05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions a Which is the null hypothesis HO The observed frequencies agree with three of the expected proportions HO The observed frequencies agree with one of the expected proportions HO The observed frequencies agree with the expected proportions OHO At least one of the observed frequencies do not agree with the expected frequencies d What is the test statistic x Round to 2 decimal places f What is the p value Round to 4 decimal places 7 39 5 16 OH1 The observed frequencies agree with one of the expected proportions H1 At least one of the observed frequencies do not agree with the expected frequencies H1 The observed frequencies agree with three of the expected proportions H1 The observed frequencies agree with the expected proportions To find the test statistic begin by converting the expected proportions in each category to a number of World Series c How many series are expected to have lasted 4 games e What are the degrees of freedom needed to find the p value

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