Introduction to Probability and Statistics for Engineers and Scientists

Problems 425

(c) DefineSSRand give its distribution.

(d) Derive a test ofH 0 :β=β 0 versusH 1 :β=β 0.

(e)Determine a 100(1−a) percent prediction interval forY(x 0 ), the response

at input levelx 0.

30.Prove the identity

R^2 =

SxY^2

SxxSYY

31.The weight and systolic blood pressure of randomly selected males in age-group

25 to 30 are shown in the following table.

Subject Weight Systolic BP Subject Weight Systolic BP

1 165 130 11 172 153

2 167 133 12 159 128

3 180 150 13 168 132

4 155 128 14 174 149

5 212 151 15 183 158

6 175 146 16 215 150

7 190 150 17 195 163

8 210 140 18 180 156

9 200 148 19 143 124

10 149 125 20 240 170

(a) Estimate the regression coefficients.

(b) Do the data support the claim that systolic blood pressure does not depend

on an individual’s weight?

(c) If a large number of males weighing 182 pounds have their blood pressures

taken, determine an interval that, with 95 percent confidence, will contain

their average blood pressure.

(d) Analyze the standardized residuals.

(e)Determine the sample correlation coefficient.

32.It has been determined that the relation between stress (S) and the number of

cycles to failure (N) for a particular type alloy is given by

S=

A

Nm

whereAandmare unknown constants. An experiment is run yielding the following

data.