Question

Hello if you could please show work for the problems and show the necessary r code for questions b and c I would appreciate it. Thank you

A shoe manufacturer compared material A and material B for the soles of shoes. Twelve volunteers each got two shoes. The left was made with material A and the right with material B. On both shoes, the material was 1 inch thick. Volunteers used the shoes normally for two months and returned them to the manufacturer. Technicians then measured the thickness of the soles and recorded the amount of wear (in microns):

Volunteer 1 2 3 4 5 6 7 8 9 10 11 12

Sole A 379 378 328 372 325 304 356 309 354 318 355 392

Sole B 372 376 328 368 283 252 369 321 379 303 328 411

They wish to test H0 : µA −µB = 0 against HA : µA −µB =/= 0, where µA and µB are the unknown population mean amounts of sole wear, using α = 0.05.

(a) Are the two samples paired or independent? Explain your answer.

(b) Make a normal QQ plot of the differences within each pair. Is it reasonable to assume a normal population of differences?

(c) Choose a test appropriate for the hypotheses above and justify your choice based on your answers to parts (a) and (b). Perform the test by computing a p-value, make a test decision, and state your conclusion in the context of the problem.

Answer 1