Givenx₁andx₂distributions that are normal or approximately normal with unknown₁and₂, the value oftcorresponding tox₁x₂has a distribution that is approximated by a Student'stdistribution. We use the convention that the degrees of freedom is approximately the smaller ofn₁1andn₂1.However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula:

d.f.

s₁²

n₁

+

s₂²

n₂

	2

1

n₁1

s₁²

n₁

	2

+

1

n₂1

s₂²

n₂

	2

wheres₁,s₂,n₁, andn₂are the respective sample standard deviations and sample sizes of independent random samples from thex₁andx₂distributions. This is the approximation used by most statistical software. When bothn₁andn₂are 5 or larger, it is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded.(a) We tested whether the population average crime rate₂in the Rocky Mountain region is higher than that in New England,₁. The data weren₁=10,x₁3.51,s₁0.87,n₂=15,x₂3.87, ands₂0.93. Use Satterthwaite's formula to compute the degrees of freedom for the Student'stdistribution. (Round your answer to two decimal places.) d.f.=