Par Inc

Topics: Standard deviation, Normal distribution, Sample size Pages: 3 (440 words) Published: February 8, 2012
Case #1
Par, Inc.
Date: October 8th 2011
Question 1
Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls

Ans:
The rational is that Par, Inc. is concerned with making sure that the market share or the new ball is comparable to the previous with the new cut-resistant, longer lasting ball. We need to compare the mean driving distance in order to be certain that the new ball efforts are worth it. Therefore we need to formulate a hypothesis test. The text tells us that Par, Inc. would like to sell the new ball once it’s comparable to the previous. Therefore: Ho: μ₁ -μ₂ ≥ 0 the mean driving distance of the new balls is greater than or equal to that of the old balls Ha: μ₁ - μ₂ ‹ 0 the mean driving distance of the new balls is less than that of the old balls, α = 0.05

CURRENT| NEW|
270.28| 267.50|
8.75| 9.90|
40| 40|

Mean
Sample Standard Deviation

N

t= (x̄₁ - x̄₂) – (μ₁ - μ₂)0
√Sp²[(1/n₁) + (1/n₂)]

Sp² = (n₁-1) s₁² + (n₂-1) s² = (40-1)(8.75) +(40-1)(9.90) ² = 6808.23 = 87.285 n₁ + n₂ - 2 40+40-2 78

Sp² = 87.285
Df= 78

t=(270.28 – 267.5) – 0 = 1.33
√87.28 (1/40 + 1/40)
t=1.33
Reject Ho: if p-Val ≤ α
P-val is .10 thus p-Val is >α = .05
Do not reject Ho:
Therefore we reject that the mean driving distance of the new balls is less than that of the old balls

Question3
Provide the following descriptive summaries of the data for each model: ONLY the means and variances and the z values.

Ans:
| Current | New |
Mean| 270.275| 267.5|
Variance| 76.6147436| 97.9487179|
Standard Error| 1.38396842| 1.56483799|

Question 4
What is the 95% confidence interval for the difference between the means of the two populations?...
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