On a national mathematics assessment test, a random sample of 120 twelfth grade students has a mean score of 150 with a standard deviation of 34.

(a) Construct a 90% confidence interval for the population mean test score.

(b) This test result prompts a school administrator to claim that the mean score for all twelfth grade students who took the test is at least 145. At α=0.05, can you reject the administrator’s claim? Interpret the decision in the context of the original claim.