Answered: players, good hip range of motion…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.8 degrees and the sample standard deviation was 5.6 degrees, whereas the sample mean and sample standard deviation for position players were 79.9 degrees and 7.2 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use

? = 0.05.

Use ?₁ for pitchers and ?₂ for position players.)

Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of
40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.8 degrees and the sample standard deviation was 5.6 degrees, whereas the
sample mean and sample standard deviation for position players were 79.9 degrees and 7.2 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers
and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use a = 0.05.
Use
H1
for pitchers and
H2
for position players.)
State the appropriate null and alternative hypotheses.
A USE SALT
O Ho: H1 - H2 = 0
Hoi H1 - H2 # 0
O Ho: H1 - 42 + 0
H: H1 - H2 = 0
O Ho: H1 - H2 < 0
H3: H1 - H2 = 0
O Ho: H1 - H2 = 0
Hoi M1- Hz>0
Ha: H1 - H2 < 0
Find the test statistic and P-value. (Use SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)
t =
P-value =
State the conclusion in the problem context.
We reject Ho. There is not convincing evidence that the mean range of motion for pitchers is less than the mean for position players.
We reject Ho: There is convincing evidence that the mean range of motion for pitchers is less than the mean for position players.
We fail to reject Ho.
There is not convincing evidence that the mean range of motion for pitchers is less than the mean for position players.
We fail to reject Ho.
There is convincing evidence that the mean range of motion for pitchers is less than the mean for position players.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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