If a person's score on a questionnaire has been found to predict observed social skills, and the linear prediction rule uses a regression constant of 16 and a regression coefficient of 3, the predicted level of social skills for a person with a score of 10 on the questionnaire is

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.