During the soccer World Cup in 2010 attendance figures (in thousands of people) of people watching...

 

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During the soccer World Cup in 2010 attendance figures (in thousands of people) of people watching games at four of the World Cup venues were recorded for some of the games at each stadium, shown as follows: (Yij - Yi.) n: (Yi. – Yi.) Stadium Attendance Crcen Point 8.9 7.2 3.1 7.1 6.7 18.16 0.06 Soccer City Ellis Park 6.6 6.9 8.2 8.3 2.30 4.05 5.6 7.3 7.2 6.3 1.94 0.04 Nelson Mandela 4.2 6.9 4.1 5.8 5.45 6.19 (a) Explain how a bootstrapping approach might be used to test the hypothesis of no differences between mean crowd attendance at the four stadiums. (b) Such a bootstrapping approach was applied, based on 2000 bootstrap replications. For each replication, the SSE, SST and the F-ratios were calculated. The F-ratios were sorted from smallest to largest, and the following are a selection of the observed values: Sample No: 50 100 500 1000 1500 1900 1950 2000 F-ratio 0.15 0.23 0.63 1.18 2.03 4.33 5.77 14.96 What conclusion should be drawn about any differences between the stadiums? (c) Compare the conclusion in the above answer with that obtained from the standard normal theory approach to ANOVA (you do not need to find an exact p-value). During the soccer World Cup in 2010 attendance figures (in thousands of people) of people watching games at four of the World Cup venues were recorded for some of the games at each stadium, shown as follows: (Yij - Yi.) n: (Yi. – Yi.) Stadium Attendance Crcen Point 8.9 7.2 3.1 7.1 6.7 18.16 0.06 Soccer City Ellis Park 6.6 6.9 8.2 8.3 2.30 4.05 5.6 7.3 7.2 6.3 1.94 0.04 Nelson Mandela 4.2 6.9 4.1 5.8 5.45 6.19 (a) Explain how a bootstrapping approach might be used to test the hypothesis of no differences between mean crowd attendance at the four stadiums. (b) Such a bootstrapping approach was applied, based on 2000 bootstrap replications. For each replication, the SSE, SST and the F-ratios were calculated. The F-ratios were sorted from smallest to largest, and the following are a selection of the observed values: Sample No: 50 100 500 1000 1500 1900 1950 2000 F-ratio 0.15 0.23 0.63 1.18 2.03 4.33 5.77 14.96 What conclusion should be drawn about any differences between the stadiums? (c) Compare the conclusion in the above answer with that obtained from the standard normal theory approach to ANOVA (you do not need to find an exact p-value).

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a First assuming no differences in the mean of 4 populations we can generate simple random s... View the full answer