4. Rumor has it that Professor Matheticka gives 5% of his students the A grade. 18% the B grade. 28%% the C grade, 32% the D grades and fail the rest. At the end of one typical semester, It was observed that in a class of 80 students, he gave 15 A's. 10 B's. 27 C's . 10 D's, and the rest F's. Does this data support the rumor ? (a) (2 points) State the null hypothesis and alternative hypothesis (b) (4 points) Find the test statistic (c) (2 points) If the type-I error a = 0.1. find the critical value(s) and shade the rejection region(s) (d) (2 points) Base on the type-I error o and rejection region(s). given above. what is your conclu sion? (Do not use p-value to draw your conclusion)