Horse Racing

Is there a dependency between the starting gate position and whether a horse finishes in "first place"? If so, which gate(s) are most likely to produce a winner?

The following data represents the starting gate positions and how the horses finished in terms of Win (first place), Place (second place), or Show (third place) in one year at

- a. Fill in the following table.
- b. Test for Independence between if a horse wins or does not win and starting gate position. Show all the steps outlined in the lecture notes. Include the table and graph.
- If a Dependency exists between if a horse wins or does not win and starting gate position, find 95% confidence intervals for the proportion of winning for each gate. You can just write the intervals, no work is needed.

Gate

1

2

3

4

5

6

7

8

9

Win

149

185

123

161

133

135

135

50

11

Place

162

227

180

202

158

112

80

52

13

Show

145

188

203

193

139

120

102

80

20

Total Starts

889

889

889

889

889

889

867

440

92

Gate

1

2

3

4

5

6

7

8

9

Win

149

Not Win

740

Gate

95% confidence interval

1

2

3

4

5

6

7

8

9

3. We want to determine which starting position is most probable to produce a winner.

- Which gate interval has the largest lower limit?
- Which gate intervals overlap this interval?
- Test if the proportions of wins from each of the gates with overlapping intervals are equal to the proportion of wins from the gate from your answer to part (a). Do separate complete hypothesis tests for each using methods from the lecture notes.

4. Conclusion: Which gate(s) are more likely to produce a winner? Explain.

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