Question

When bonding​ teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field.​ However, there is concern that the new bonding adhesive is not as strong as the current​ standard, a composite adhesive. Tests on a sample of 9 extracted teeth bonded with the new adhesive resulted in a mean breaking strength​(after 24​ hours) of overbarx=5.78 Mpa and a standard deviation ofs=0.41Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.35 ​Mpa, the mean breaking strength of the composite adhesive.

a. Set up the null and alternative hypotheses for the test. Choose the correct answer below.

A. H0​: μ = 5.78 vs.Ha​:μ ≠ 5.78

B. H0​: μ = 5.78vs. Ha​: μ < 5.78

C.

H0​:μ =6 .35 vs.Ha​: μ < 6.35

Your answer is correct.

D.H0​: μ or ≥ 6.35 vs.Ha​:μ < 6.35

E. H0​:= 6.35 vs. Ha​: μ ≠ 6.35

F. H0​:μ = 6.35 vs.Ha​: μ > 6.35

b. Find the rejection region for the test using α=0.01.

Choose the correct answer below.

A. t > − 2.896

B. t > 3.355

C.t<−2.896

D.t > 2.896

E.t >−3.355

F.t < 2.896

G.t < 3.355

H.t <− 3.355

Answer 1