Problems 423
Shear Strength (psi) Weld Diameter (.0001 in.)
370 400
780 800
1,210 1,250
1,560 1,600
1,980 2,000
2,450 2,500
3,070 3,100
3,550 3,600
3,940 4,000
3,950 4,000(c) Test the hypothesis that the slope of the regression line is equal to 1 at the .05
level significance.
(d) Estimate the expected value of shear strength when the weld diameter is .2500.
(e) Find a prediction interval such that, with 95 percent confidence, the value
of shear strength corresponding to a weld diameter of .2250 inch will be
contained in it.
(f ) Plot the standardized residuals.
(g) Does the plot in part (f) support the assumptions of the model?
27.A screw manufacturer is interested in giving out data to his customers on the
relation between nominal and actual lengths. The following results (in inches)
were observed.Nominalx Actualy
1
4 .262 .262 .245
1
2 .496 .512 .490
3
4 .743 .744 .751
1 .976 1.010 1.004
114 1.265 1.254 1.252
112 1.498 1.518 1.504
134 1.738 1.759 1.750
2 2.005 1.992 1.992(a) Estimate the regression coefficients.
(b) Estimate the variance involved in manufacturing a screw.
(c) For a large set of nominal 1-inch screws, find a 90 percent confidence interval
for the average length.