Discussion:
Q: In a statistics lecture, students are asked whether or not they enjoyed doing statistics. Random sample of 50 students was taken and 30 of them said that they enjoyed doing statistics. The lecturer claimed that more than 50% of the students enjoyed doing statistics.
(i) Test, at the 5% level of significance, whether or not the lecturer's claim is reasonable. State the null and alternative hypotheses of the test.
(ii) Find a 95% and a 99% confidence intervals for the true proportion of students who enjoyed doing statistics. Which one is wider? Why?
(iii) If the lecturer would like the difference between the true proportion and the sample proportion to be less than 5%, what is the minimum number of students he should ask Use alpha = 0.05