Par Inc
Case Problem: Par, Inc.
Section I: Summary
Par, Inc., a major manufacturer of golf equipment believes that a cut-resistant, longer lasting golf ball could increase their market share. In addition to the requirement that the ball be longer lasting, they wanted to ensure that the new coating would not reduce driving distances, and would be comparable to the current product.
Section II: Relevant Statistical Results
Statistic
Current Model
New Model
Sample Mean
270.275
267.500
Standard Error
1.3840
1.5648
Standard Deviation
8.7530
9.8969
Sample Size
40
40
Confidence Level (95%)
2.62
3.14
Degrees of freedom
39
39 t = 1.33
Comparisons
1. A two tail hypothesis test was conducted based on the sample studies of 40 current and 40 new golf balls.
The testing was performed with a machine designed to hit the ball the same every time. Both samples were tested with the same machine to ensure consistent strikes.
2. The hypothesis for Par, Inc. to compare the driving distances of the current and new golf balls is:
H0: µ1 - µ2 ≥ 0 (mean distance of new greater than or equal to the old)
Ha: µ1 -µ2 < 0 (mean distance of new less than old)
3. Statistical basis n1 = 40 n2 = 40 x1 = 270.28 x2 = 267.5 s1 = 8.75 s2 = 9.90 α = .05 df = 78 t = (270.28 – 267.5) – 0 = 1.33
P-value = .10
P-value > .05 (or α); do not reject H0
4. The 95% confidence interval for the sample mean driving distance for current golf balls is 267.66 to 272.90. The 95% confidence interval for the sample mean driving distance for the new model is 264.36to 270.64. The 95% confidence interval for the difference between the sample means is between -1.62 and 7.17.
5. I do not believe we need a larger sample size. If we had a larger sample the standard deviations become smaller, not larger. It would only bring the point values closer together.
Section III: Recommendation
Since the P-value is greater than .05, we do not reject H0. This means that the best course of action for Par, Inc. is to
Section I: Summary
Par, Inc., a major manufacturer of golf equipment believes that a cut-resistant, longer lasting golf ball could increase their market share. In addition to the requirement that the ball be longer lasting, they wanted to ensure that the new coating would not reduce driving distances, and would be comparable to the current product.
Section II: Relevant Statistical Results
Statistic
Current Model
New Model
Sample Mean
270.275
267.500
Standard Error
1.3840
1.5648
Standard Deviation
8.7530
9.8969
Sample Size
40
40
Confidence Level (95%)
2.62
3.14
Degrees of freedom
39
39 t = 1.33
Comparisons
1. A two tail hypothesis test was conducted based on the sample studies of 40 current and 40 new golf balls.
The testing was performed with a machine designed to hit the ball the same every time. Both samples were tested with the same machine to ensure consistent strikes.
2. The hypothesis for Par, Inc. to compare the driving distances of the current and new golf balls is:
H0: µ1 - µ2 ≥ 0 (mean distance of new greater than or equal to the old)
Ha: µ1 -µ2 < 0 (mean distance of new less than old)
3. Statistical basis n1 = 40 n2 = 40 x1 = 270.28 x2 = 267.5 s1 = 8.75 s2 = 9.90 α = .05 df = 78 t = (270.28 – 267.5) – 0 = 1.33
P-value = .10
P-value > .05 (or α); do not reject H0
4. The 95% confidence interval for the sample mean driving distance for current golf balls is 267.66 to 272.90. The 95% confidence interval for the sample mean driving distance for the new model is 264.36to 270.64. The 95% confidence interval for the difference between the sample means is between -1.62 and 7.17.
5. I do not believe we need a larger sample size. If we had a larger sample the standard deviations become smaller, not larger. It would only bring the point values closer together.
Section III: Recommendation
Since the P-value is greater than .05, we do not reject H0. This means that the best course of action for Par, Inc. is to