Of a sample of 500 students, 200 oppose changing the logo of the school, whereas out of 500 professors, 150 feel the same. Test whether there is any significant difference between the opinion of professors and students.

a) State the hypotheses and write the meaning of the hypotheses.

b) Compute the associated standardized statistic, corresponding p-value and the critical value at a 5% significance level.

c) Indicate the conclusions of your test in terms of the problem.