Question

An article in the Journal of Strain Analysis (Vol 18, No. 2, 1983) compares several procedures for predicting the shear strength for steel plate girders. Data for the ratio of predicted to observed load for two of these procedures on 9 girders are collected using paired comparative experiment are displayed as follows:

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	1.2	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

(a) Is there any evidence to support a claim that there is a difference in mean performance of the two methods? Using α = 0.05?

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

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

Answer 1

using minitab>stat>basic stat>paired t test

we have

Paired T for Karlsruhe Method - Lehigh Method

N Mean StDev SE Mean
Karlsruhe Method 9 1.3401 0.1460 0.0487
Lehigh Method 9 1.0662 0.0494 0.0165
Difference 9 0.2739 0.1351 0.0450

95% CI for mean difference: (0.1700, 0.3777)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 6.08 P-Value = 0.000

a ) here the degree of freedom is 8

t tabulated value from t table is 2.306

since 6.08 >2.306 so we conclude that yes  there is sufficient evidence to support a claim that there is a difference in mean performance of the two methods.

b ) p value is 0.000

c )  a 95% confidence interval for the difference in mean ratio of predicted to observed load is (0.1700,0.3777)