Researchers calculated the following summary statistics from two simple random samples from two distinct populations:
x1= 3.647, s1 = 1.9, n1 = 17
x2= 2.529, s2 = 1.7, n2 = 17
When the researchers computed the degrees of freedom by hand, they got k = 16, and for the P-value, they got p = .0447. However, their computer software gave them k = 31.60 and p = .0402.
Which of the following is most likely true about the difference in P-values?
A. Computer software gives a larger value for k and a lower P-value, which gives you a higher power of the test.
B. The computer software gave a smaller P-value because it uses pooling, and so gives you a more accurate estimate of degrees of freedom.
C. When you compute degrees of freedom, taking the smaller sample size minus one gives you a better approximation of a t distribution.
D. Computer software gives a more accurate P-value and, therefore, gives you a lower power of the test.
E. The researchers made an error when they calculated the degrees of freedom by hand.