Wilmer thinks that NBA players in general are taller than hi

Wilmer thinks that NBA players, in general, are taller than high school basketball players. He has measured 4 NBA players, with heights 80, 84, 73, and 75 inches. He has measured 6 high school basketball players, with heights 77, 72, 74, 78, 73, and 76 inches.

He calculates a sample mean of 78 for the NBA players and 75 for the high school players. The NBA sample mean minus the high school sample mean is 3.

Wilmer creates a randomization test to show this theory, using the test statistic described above.

What is the p-value? Round to the nearest percent.

A. 12%

B. 14%

C. 16%

D. 18%

Thank you for the help!

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 > u2
Test Statistic
X(Mean)=78
Standard Deviation(s.d1)=4.967 ; Number(n1)=4
Y(Mean)=75
Standard Deviation(s.d2)=2.366; Number(n2)=6
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =78-75/Sqrt((24.67109/4)+(5.59796/6))
to =1.13
| to | =1.13
P-Value:Right Tail -Ha : ( P > 1.1258 ) = 0.17109

ANS: D. 18%