A professor in the faculty of education is studying education levels of adults in the province. She hypothesizes that highest level of education achieved by people in province has following:

education didn't finish high school high school diploma bachelors degree postgraduate

level

proportion 0.08 0.48 0.39 0.05

in a random, sample of 500 people in province, 50 didn't finish high school, 218 have high school diploma, 202 have bachelor's degree and 30 have postgraduate.

a) conduct hypothesis test at 5% level of significance to investigate professor's suspicion. you only need to show calculation for one of the cells. Calculate value of test statistic and p-value and provide properly conclusion.

b) show how you arrive at same conclusion if you had conducted test using critical value method.