An article in the Journal of Swain Analysis (vol. 18, no. 2, 1983) compares several pro-cedures for predicting the shear strength for steel plate girders. Data for nine girders in the form of the ratio of predicted to observed load for two of these procedures, the Karls-ruhe and Lehigh methods, are as follows:

 

(a) Is there any evidence to support a claim that there is a difference in mean perfor-mance between the two methods? Use α = 0.05.

(b) What is the P-value for the test in part (a)?

(c) Construct a 95 percent confidence interval for the difference in mean predicted to observed load.

(d) Investigate the normality assumption for both samples.

(e) Investigate the normality assumption for the difference in ratios for the two methods.

(f) Discuss the role of the normality assumption in the paired t-test.

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Girder Karlsruhe Method Lehigh Method S1/1 1.186 1.061 S2/1 1.151 0.992 S3/1 1.322 1.063 S4/1 1.339 1.062 S5/1 1.200 1.065 S2/1 1.402 1.178 S2/2 1.365 1.037 S2/3 1.537 1.086 S2/4 1.559 1.052