A mechanical engincering professor is interested in time it would take for students to study, learn and run codes in MATLAB. For this aim professor got a sample of $40$ students and reported the average amount of time to learn and run code as $35\mathrm{.}5$ hours with a standard deviation of $3\mathrm{.}1$ hours. Based on these findings;

a$)$ Is there evidence that time to learn and run MATLAB code greater than $36$ hours? $0\mathrm{.}05)$ Please show rejection and non$-$rejection regions properly. $(10pts)$

b$)$ What is the interpretation of TYPE I error in this hypothesis? $(10$ pts$)$