Question

A golf ball manufacturer desires to compare the distance traveled by golf balls using four unique designs. Fifteen balls were manufactured and each was brought to the local golf course for testing by the local pro. The order of the golf balls hit by the professional was randomized so the pro did not know which ball was being hit. All 60 balls were hit over a short time period to reduce any potential environmental effects. Use the data provided to answer the following questions: 1. At the 0.05 level of significance is there evidence of a difference in the mean distances traveled by the golf balls with different designs? 2. Do the results in question 1 indicate that it is appropriate to use the Tukey-Kramer procedure to determine which designs differ in mean distances? 3. If the golf ball manufacturer wished to build the golf ball with the greatest distance, which design should the firm select?

A | B | C | D | |

1 | 221.84 | 244.90 | 247.89 | 233.40 |

2 | 223.58 | 241.69 | 245.09 | 238.08 |

3 | 221.70 | 247.03 | 249.27 | 234.44 |

4 | 219.82 | 245.69 | 241.78 | 240.98 |

5 | 225.42 | 238.09 | 246.75 | 227.75 |

6 | 219.14 | 240.68 | 248.48 | 229.99 |

7 | 222.30 | 240.81 | 238.19 | 237.92 |

8 | 221.15 | 251.92 | 253.16 | 246.68 |

9 | 219.87 | 236.01 | 245.52 | 229.60 |

10 | 226.72 | 250.52 | 242.02 | 230.64 |

11 | 240.39 | 259.87 | 263.52 | 255.99 |

12 | 236.36 | 264.17 | 259.96 | 259.11 |

13 | 235.62 | 258.78 | 267.16 | 247.28 |

14 | 237.78 | 270.86 | 272.19 | 265.23 |

15 | 243.77 | 269.36 | 260.22 | 247.99 |

Answer #1

**Part
1**: -

A one way ANOVA was applied to check if there is any significant difference in the mean distances traveled by the golf balls with different designs.

Null Hypothesis : u_{1} = u_{2} = u_{3}
= u_{4}

Alternate Hypothesis : Not all the means are equal

The data points were analysed in Excel and the output of ANOVA (single factor) is shown below: -

From the output it can be analysed that P value is less than 0.05, hence Null Hypothesis should be rejected.

Hence, it can be concluded that there is a significance difference in the mean distances traveled by the golf balls with different designs.

A major manufacturer of golf equipment has designed a new model
of golf ball with a cut resistant coating. However there is a
question concerning the mean driving distance in yards of the new
model golf balls as compared to their older model. A sample of each
type of golf ball is tested for driving distance and the results
are found in the table below. Test to see if the mean driving
distance is changed by the new coating and...

Ten professional golfers are asked to hit each of two brands of
golf ball with their drivers. The golfers do not know which brand
they are hitting, and the order in which they hit the balls is
determined by flipping a coin. The distances of their drives are
listed in the table.
Golfer
Brand 1
Brand 2
1
265
268
2
281
283
3
260
257
4
274
277
5
269
270
6
288
291
7
271
275
8
270...

Par Inc., is a major manufacturer of golfequipment. Management
believes that Par’s market share could be increased with the
introduction of a new ball designed to fly straighter and to be
more durable. Therefore, the research group at Par has been
investigating a new golf ball coating designed to achieve this
goal. The tests with the new ball have been promising. One of the
researchers voiced a concern about the potential for the new
coating to have a negative effect...

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