Fatigue specimens. Three labs tested fatigue specimens at two strain ranges. The failure of a specimen occurs either within or outside the length of the strain gage. According to specimen geometry and engineering theory, the expected fraction of failures within the gage length is po =4/9 for any strain range and lab. The fractions y / n of specimens failing within the gage are tabulated below.
(a) Which of the six observed fractions differ significantly from the theoretical po =4/9?
(b) For Lab 1, do the observed fractions at Strains 1 and 2 differ significantly? For Lab 2? For Lab 3?
(c) For Strain I , do the fractions for the three labs differ significantly? Simultaneously compare ( I ) all three labs and ( 2 ) each pair of labs.
(d) Do (c) for Strain 2.
(e) Pool data from each lab and compare the three labs as in (c).
( f ) State your overall conclusions.
(g) Comment on the adequacy for practical purposes of any approximate tests or confidence intervals you used.