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# The Two-Sample t Test and Confidence Interval

Math Probability and Statistics II
Chapter 9.2 Topic: The Two-Sample t Test and Confidence Interval

Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article "Forces on the Hand in the Tennis One-Handed Backhand" (Intl. J. of Sport Biomechanics, 1991: 282 - 292) reported the force (N) on the hand just after impact on a one-handed backhand drive for six advanced players and for eight intermediate players.

Type of Player Sample Size Sample Mean Sample SD
1. Advanced 6 40.3 11.3
2. Intermediate 8 21.4 8.3

In their analysis of the data, the authors assumed that both force distributions were normal. Calculate a 95% CI for the difference between true average force for advanced players (u_1) and true average force for intermediate players (u_2). Does your interval provide compelling evidence for concluding that the two u's are different? Would you have reached the same conclusion by calculating a CI for u_2 - u_1 (ie. by reversing the 1 and 2 labels on the two types of players)? Explain.

#### Solution Summary

This solution shows the calculations for testing the two means with interpretation of results in an attached Word file.

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