Project: Chi-Square

Is there a dependency between the starting gate position and whether a horse finishes "first" or "in the money"?

Problem I.
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 2007) was compiled at

in Maywood, IL.

Gate	1	2	3	4	5	6	7	8	9
Win	182	181	150	181	157	81	47	35	67
Place	178	196	171	137	153	91	69	39	40
Show	142	168	165	132	147	112	101	65	47
Total Starts	1,077	1,077	1,077	1,077	1,077	1,069	1,010	785	429

A. Show all four steps for each hypothesis test needed to test the claim. 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)".

Gate	1	2	3	4	5	6	7	8	9
Win	182	181	150	181	157	81	47	35	67
Not Win	895	896	927	896	920	988	963	750	362

B. If a dependency exists between "winning (first)" and "starting position". Find 95% confidence
intervals for the percentage of winning for each gate.
Hint: See lesson on confidence intervals for proportions .

C. According to your analysis, which starting position is most probable to produce a winner?

D.   Show all four steps for each hypothesis test needed to test the claim. At a 0.05 level
      of significance, test for the existence of a dependency between starting gate position and
      whether a horse finishes "in the money" (win, place or show" or "out of the money".)

Gate	1	2	3	4	5	6	7	8	9
In the Money	502	545	486	450	457	284	217	139	154
Not In the Money	575	532	591	627	620	785	793	646	266

E. If a dependency exists between "finish in the money (win-place-show)" and "starting position".
Find a 95% confidence intervals for the percentage of "finishing in the money" for each gate.

F. According to your analysis, which starting position is most probable to produce a horse
"finishing in the money"?

Problem II.
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 2007) was compiled at

in Crete, IL.

Gate	1	2	3	4	5	6	7	8	9	10
Win	267	285	260	257	314	250	161	135	81	49
Place	281	259	269	241	282	266	172	148	84	50
Show	272	273	255	260	270	242	206	142	88	45
Total Starts	2,052	2,052	2,052	2,051	2,040	2,001	1,805	1,485	1,016	553

Gate	1	2	3	4	5	6	7	8	9	10
Win	267	285	260	257	314	250	161	135	81	49
Not Win	1,785	1,767	1,792	1,794	1,726	1,751	1,644	1,350	935	504

C. According to your analysis, which starting position is most probable to produce a winner?

Gate	1	2	3	4	5	6	7	8	9	10
In the Money	820	817	784	758	866	758	539	425	253	144
Not In the Money	1,232	1,235	1,268	1,293	1,174	1,243	1,266	1,060	763	409

E. If a dependency exists between "finish in the money (win-place-show)" and "starting position".
Find a 95% confidence intervals for the percentage of "finishing in the money" for each gate.

F. According to your analysis, which starting position is most probable to produce a horse
"finishing in the money"?

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