Chris is evaluating two preliminary designs on a drill shaft foundation, submitted recently by two competing engineering firms (AAA, and BBB), to transfer large amount of axial and lateral loads from a newly proposed multi-purpose structure. To obviate predictable in-situ settlement of drilled-shafts due to sedimentary silty clay soil, i.e., grayish ocean muck, both designs proposed of using a sandstone-socket supported shaft method, however each design is based on different shaft materials and drilling techniques. Cost and project duration estimates [for all the heavy equipment's, procurements, sandstone sockets, shafts, drilling and other field operations, etc. for the project] from two companies are identical according to executive summaries received by Chris.

Subsequently, per request from Chris, both firms promptly submitted their own test data on unconfined compressive strength of core (in psi) corresponding to the bond of the proposed sandstone-socket supported shafts, tested and collected under a similar soil condition asimilar to the proposed site. Preliminary Shapiro-Wilk p-values of test data were 0.7629 for AAA and 0.7663 for BBB, respectively, at a 95% level of confidence.

(1) Evaluate whether both proposed designs would achieve the same mean unconfined compressive strength of core (in psi) or not at .05 under equal (σ1²=σ2²) *AND* unequal (σ1²≠σ2²) variance assumptions.

(2) If Chris would make the final design selection purely based on the higher unconfined compressive strength of core, which company's design would be your recommendation?