Project Chi-Square Test for Independence
Is there a dependency between the starting gate position and whether a horse finishes in “first place”?
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). The data (all races ran in 2009) was compiled at Chicago Harness in Maywood, IL.
Gate
1
2
3
4
5
6
7
8
9
Win
261
223
163
180
149
96
62
44
15
Place
202
227
180
162
158
112
80
52
13
Show
193
188
203
145
139
120
102
80
20
Total Starts
1,189
1,189
1,189
1,189
1,189
1,189
1,167
992
106
A. At a 0.05 level of significance, test for the existence of this dependency between starting gate position and whether a horse finishes “Win (first)” or “Not win (not first)”.
Show all the steps for the hypothesis test: state the null and alternative, use your calculator to get the P-value, make the decision and state the conclusion.
Gate
1
2
3
4
5
6
7
8
9
Win
261
223
163
180
149
96
62
44
15
Not Win
928
966
1,026
1,009
1,040
1,093
1,105
948
91
Part A. At a 0.05 level of significance, test for the existence of this dependency between starting gate position and whether a horse finishes “Win (first)” or “Not win (not first)”. Put the data into a 2 by 9 matrix and do a chi-square test for independence.
1.) State the null and alternative hypotheses and indicate where the claim is.
2.) Perform the test by finding the p-value (use your calculator).
3.) Make the appropriate decision to reject or fail to reject, Indicate why you made this decision.
4.) State the conclusion about the claim for this hypothesis test.
Part B. If a dependency exists between “winning (first)” and “starting position”. Find 95% confidence intervals for the percentage of winning for each gate.
Hint: Use 1-PpropZInt to construct a confidence intervals for proportions.
Gate
95% confidence interval
1
2
3
4
5
6
7
8
9
Part C. 1.) Which starting position is most probable to produce a winner?
Hint: Which gate interval has the largest lower limit?
2. Which gate intervals overlap this interval?
3. Using the 2-PropZTest and a 0.05 level of significance test whether the proportions for the overlapping interval are equal to the interval with the largest lower limit, one at a time. Show all the steps for each hypothesis test. Test1:
p-value= ___________________
Do you reject or Fail to reject the null hypothesis?
Conclusion about this claim:
Test2:
p-value= ___________________
Do you reject or Fail to reject the null hypothesis?
Conclusion about this claim:
4. Final Conclusion: Which gate(s) are most probable to produce a winner?
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