New Cut-Resistant Ball
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This analysis reviews Pars new cut-resistant golf ball by comparing it to the current model. The new cut-resistant ball will last longer than the current model due to its cut-resistant design. The purpose of this analysis is to test whether or not the new cut-resistant golf ball offers the same driving distances as the current ball.
In order to test the driving distances of both the new and current model golf balls, a test was constructed using a mechanical hitting machine. The test involved the hitting machine driving 40 golf balls of each model and the driving distance was recorded. The statistical analysis in this document compares the results of this test data and recommends a course of action based on the results. The Minitab statistical software package is used to execute the analysis.
THE HYPOTHESIS TEST
This research tests the assumption the driving distance for new model golf ball is at least as far as the older model golf ball. This test is making inferences about the difference between two population means were the population standard deviations, σ1 and σ2, are unknown. The sample standard deviation will be calculated to estimate the population standard deviations. Since the population standard deviation is unknown the t distribution is used.
For this test the Confidence Interval is 95% and α = .05. The sample size for both models is n = 40.
µ1 = The mean driving distance for the current model golf balls
µ2 = The mean driving distance the new model golf balls
In this analysis the team tests Par Researchs assumption that the new model will perform at least as well as the older model in driving distance. It is not enough to merely test if the two means are different. In this case the null hypothesis (H0) expresses Par Researchs belief that the new model golf ball will perform at least as well as the older model. The alternative hypothesis (Ha) is that the assumption is incorrect.
Hypothesis:
H0: µ1 – µ2 <= 0
Ha: µ1 - µ2 > 0
For this upper tail test using the t distribution we reject H0 if the p-value < .05. If the p-value >= .05 then we fail to reject the H0.
RESULTS OF THE HYPOTHESIS TEST
Two-Sample T-Test and CI: Current, New
Two-sample T for Current vs New
N Mean StDev SE Mean
Current 40 270.27 8.75 1.4
New 40 267.50 9.90 1.6
Difference = mu (Current) – mu (New)
Estimate for difference: 2.77
95% lower bound for difference: -0.70
T-Test of difference = 0 (vs >): T-Value = 1.33 P-Value = 0.094 DF = 76
With an upper tail test the p-value = 0.094 and the t-value = 1.33. Since 0.094 > 0.05 we fail to reject the null hypothesis, H0. H0 expresses Par Researchs assumption that the new model golf ball will perform at least as well as the older model, and this analysis supports that conclusion.
The following histograms (Figure 1 and Figure 2) show the distribution for both the current and new golf ball model driving distance data. The histograms show that the data is not severely skewed, although each shows a slight right skew.
STATISTICAL SUMMARIES FOR THE TEST DATA
Overall the descriptive statistics for the current and new model golf balls show similar results in the driving distance data.
Descriptive Statistics: Current, New
Variable Mean SE Mean StDev CoefVar Minimum Q1 Median Q3
Current 270.27 1.38 8.75 3.24 255.00 263.00 270.00 275.75
New 267.50 1.56 9.90 3.70 250.00 262.00 265.00 275.50
Variable