A business school claims that students who complete 3-month typing course can type mean of more than 1200 word an hour. A random sample of 25 students who completed this course typed a mean of 1125 words an hour, with a standard deviation of 85 words. Assume that typing speeds for all students who complete course have an approximately normal distribution.

(a) Using the P-value method and a significance level of 1%, is there evidence to support the business school's claim?

(b) Construct the corresponding confidence interval and explain how it supports your conclusion in (a).