93. Suppose that we have y1, . . . , ym  N(m1, s2), ym1, . . . , ymn  N(m2, s2), and all m  n observations are independent. These are the assumptions of the pooled t procedure in Section 10.2. Let k  1,

x11.5, . . . , xm1.5, xm1,1.5, . . . , xmn,1.5.
For convenience in inverting XX assume mn.

a. Obtain and from [XX]1 Xy.

b. Find simple expressions for , SSE, s, c11.

c. Use parts

(a) and

(b) to nd a simple expression for the 95% con dence interval [Equation (12.25)] for b1. Letting be the mean of the rst m observations and be the mean of the next n observations, your result should be which is the pooled variance con dence interval discussed in Section 9.2.

d. Let m  3 and n  3, with y1  117, y2  119, y3  127, y4  129, y5  138, y6  139. These are the prices in thousands for three houses in Brookwood and then three houses in Pleasant Hills. Apply parts (a), (b), and

(c) to this data set.