The height of American Dobermans is normally distributed. A random sample of 20 American Dobermans is taken and their heights result in a mean of 27.5 in. and a standard deviation of 1.2 in.

a.) At a 0.10 level of significance, test the claim that the American Doberman mean height is less than the European Doberman mean height of 28in.

(Please set up the hypotheses, indicate the claim and the direction of the test, give the test statistics, state the decision, and provide an interpretation in the context of the original claim.)

b.) According to your decision in part a, what type of error can happen, and what could be the consequences of this error?