Given x and x2 distributions that are normal or approximately normal with unknown , and o, the value of t corresponding to x-x2 has a distribution that is approximated by a Student's t distribution. We use the convention that the degrees of freedom is approximately the smaller of n - 1 and n 1. However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula: - d.f.= "1 A1 2 1 + 2 2 where s, S, n, and n are the respective sample standard deviations and sample sizes of independent random samples from the x and x2 distributions. This is the approximation used by most statistical software. When both n 12 are 5 or larger, It is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded. and R (a) We tested whether the population average crime rate u in the Rocky Mountain region is higher than that in New England, . The data were n = 16, x = 3.51, s = 1.09, n = 19, x3.87, and s = 1.04. Use Satterthwaite's formula to compute the degrees of freedom for the Student's t distribution. (Round your answer to two decimal places.) d.f.=4.58 X (b) Previously, you followed the convention that degrees of freedom d.f. = smaller of n - 1 and n- 1. Compare this value of d.f. with that found with Satterthwaite's formula. O The previous method leads to a d.f. that is always less than or equal to that computed by Satterthwaite's formula. O The previous method leads to a d.f. that could be less than or greater than that computed by Satterthwaite's formula. The previous method leads to a d.f. that is always greater than or equal to that computed by Satterthwaite's formula. O The previous method leads to a d.f. that is always equal to that computed by Satterthwaite's formula.