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wrote...
Posts: 219
2 weeks ago
Most people are definitely dominant on one side of their body - either right or left. For some sports being able to use both sides is an advantage, such as batting in baseball or softball. In order to determine if there is a difference in strength between the dominant and non-dominant sides, a few switch-hitting members of some school baseball and softball teams were asked to hit from both sides of the plate during batting practice. The longest hit (in feet) from each side was recorded for each player. The data are shown in the table below. Does this sample indicate that there is a difference in the distance a ball is hit by batters who are switch-hitters?


Create and interpret a 95% confidence interval.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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wrote...
Posts: 237
2 weeks ago
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Under these conditions the sampling distribution of the differences can be modeled by a Student's t-model with (n - 1) = 18 degrees of freedom. We will use a paired t-interval.
We find from the data:  n =19 pairs , = 25.1 feet, and sd = 2.31 feet.
We estimate the standard deviation of using: SE() = = = 0.53.
The 95% critical value for is t18 is 2.101 (from table).
The margin of error: ME = t*18 × SE() = 2.101(0.53) = 1.11
So the 95% confidence interval is 25.1 ± 1.11, or an interval of (23.99, 26.22) feet.

We are 95% confident that hits from the dominant side will average between 24.0 and 26.2 feet longer than hits from the non-dominant side of the plate.
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2 weeks ago
This calls for a celebration Person Raising Both Hands in Celebration
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