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Posts: 189
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?


Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
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2 weeks ago
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Let d = difference in the hit lengths between the dominant side and the non-dominant side of the plate.
H0: μd = 0 The mean difference in the hit lengths (in feet) is zero.
HA: μd > 0 The mean difference in the hit lengths (in feet) is greater then zero.
* Paired data: The data are paired because they are measurements on the same individual from the dominant side and the non-dominant side of the plate.
* Independence: The hit length by any individual is independent of the hit length of other  individuals, so the differences are independent.
* Randomization: We assume these switch-hitters, though not randomly selected, are representative of all switch-hitters.
* 10% condition: Our inference is about hit lengths from dominant and non-dominant sides, not about individuals, so we do not need to check this condition.
* Nearly Normal condition: The histogram of the differences is unimodal and symmetric.

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-test.
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.
t18 = = = 47.4 P = P(t18 > 47.4) < 0.0001
With a P-value this small, we can reject the null hypothesis. We have strong evidence that hits tend to be longer from the dominant side of the plate.
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