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In: Statistics and Probability

A amateur golfer wishes to determine if there is a difference between the drive distances of...

A amateur golfer wishes to determine if there is a difference between the drive distances of her twofavorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hitsfourteen balls with driver A and 10 balls with driver B. The drive distances (in yards) for the trialsare show below.Driver A259198218229227233224266261207236193260217Driver B174257221272273201216299210256Assume that the populations are approximately normal. Construct a 95% confidence interval for thedifference between the mean drive distances for the two drivers.

Solutions

Expert Solution

For Driver A: = 237.9, s1 = 39.17, n1 = 14

For Driver B: = 230.57 , s2 = 23.73, n2 = 10

Since s1/s2 = 39.17/23.73 = 1.65 (it lies between 0.5 and 2) we used the pooled standard deviation

The Pooled Variance is given by:

df = n1 + n2 – 2 = 14 + 10 – 2 = 22

The tcritical (2 tail) for = 0.05, df = 22 is 1.717

The Confidence Interval is given by (   - ) ME, where

  - = 237.9 – 230.57 = 7.33

The Lower Limit = 7.33 - 23.97 = -16.641

The Upper Limit = 7.33 + 23.97 = 31.301

The 95% Confidence Interval is (-16.641 , 31.301)

orchestra answered 2 years ago
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