Par Inc is a manufacturer of golf equipment and has develope

Par, Inc. is a manufacturer of golf equipment and has developed a new golf ball that has been designed to provide extra distance.? In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor. We want to determine whether or not there is a significant difference between the two balls

Solution

Sample #1                     Sample #2

                                                                           Par, Inc.         Rap, Ltd.

Sample Size                             n₁ = 120 balls               n₂ = 80 balls

Mean                                               = 235 yards           = 218 yards

Standard Deviation                s₁ = 15 yards                s₂ = 20 yards

Point Estimate of the Difference Between Two Population Means

                                m₁ = mean distance for the population of

                                          Par, Inc. golf balls

                                m₂ = mean distance for the population of

                                          Rap, Ltd. golf balls

                Point estimate of m₁ - m₂ =            = 235 - 218 = 17 yards.

95% Confidence Interval Estimate of the Difference Between Two Population Means: Large-Sample Case, s₁ ands₂ Unknown

                Substituting the sample standard deviations for the population standard deviation:

X1-x2+ z sqrt (sigma1^2 /n1 + sigma2^2 /n2 )=17+ - 1.96 sqrt (15^2 /120 + 20^2 /80)

                                   = 17 + 5.14 or 11.86 yards to 22.14 yards.

                We are 95% confident that the difference between the mean driving distances of Par, Inc. balls and Rap, Ltd. balls lies in the interval of 11.86 to 22.14 yards