The Program Director of a business degree in a public university is responsible for the learning experience of 1,230 new students recently enrolled. He is committed to recruit more lecturers in the economics discipline if more than 8% of his new students are likely to elect economics as a study major. To investigate this, the Program Director commissioned for a survey to be conducted amongst 300 randomly selected new students. They were asked which major they are likely to choose. 33 students identified economics as their most preferred major.

1. Suppose you were a post-graduate student working as the research assistant of the Program Director. Assist in performing a hypothesis test at the 10% level of significance to address the problem specified above. Display the six steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test. (6 marks)
2. Specify the decision rule to use in the p-value method hypothesis testing. Calculate the p-value of the test above. Display working. (2 marks)
3. Following the completion of the test in part a), would you suggest to the Program Director to recruit more economics lecturers? Yes or no? Why? (1 mark)
4. What is the required condition for ensuring that the sampling distribution of the sample proportion is approximately normally distributed? Check if the condition is satisfied in the hypothesis testing that you just completed. (1 mark)