Research has shown that good hip range of motion and strengt

Research has shown that good hip range of motion and strength in throwing athletes results in improved performance and decreased body stress. The article ``Functional Hip Characteristics of Baseball Pitchers and Position Players\'\' (\\textit{Am. J. Sport. Med.}, 2010: 383-388) reported on a study involving samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean trail leg total arc of motion (degrees) was 75.6 with a sample standard deviation of 5.9, whereas the sample mean and sample standard deviation for position players were 79.6 and 7.6, respectively. Assuming normality, test appropriate hypotheses to decide whether true average range of motion for the pitchers is less than that for the position players (as hypothesized by the investigators). In reaching your conclusion, what type of error might you have committed?

Solution

Set Up Hypothesis
Null, no significance in average range of motion for the pitchers
and the position players Ho: u1 > u2
Alternate, true average range of motion for the pitchers is less
than that for the position players - H1: u1 < u2
Test Statistic
X(Mean)=75.6
Standard Deviation(s.d1)=5.9 ; Number(n1)=40
Y(Mean)=79.6
Standard Deviation(s.d2)=7.6; Number(n2)=40
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =75.6-79.6/Sqrt((34.81/40)+(57.76/40))
to =-2.63
| to | =2.63
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 39 d.f is 1.685
We got |to| = 2.62939 & | t | = 1.685
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Left Tail - Ha : ( P < -2.6294 ) = 0.00609
Hence Value of P0.05 > 0.00609,Here we Reject Ho

we have evidence to indicate that true average range of motion for the pitchers
is less than that for the position players