(12 marks) Suppose that on a typical day the proportion of students who drive to university is 0.3, the proportion who bike is 0.25, the proportion who take the bus is 0.35, and the remaining 0.1 come to the university some other way (for example walk, get a ride). The university sponsors a day "spare the air" to encourage people not to drive to university on that day. Do the proportions of students using each mode of transportation on that day differ from the norm? In order to answer this question, they obtain a random sample of 300 students that day and ask them how they got to the university. The results are

Method of transportation Drive Bike Bus Other

Frequency 75 100 100 25

Conduct a statistical test, testing the relevant hypotheses to answer the question and state the answer you found