A statistics module has been running for many years and, in the past, it has been found that each year the number of students passing the exam has distribution Bi(n. 0.75), where n are the number of students taking the module that year. A lecturer is teaching the module for the first time and 105 out of 150 students pass the exam. Perform a hypothesis test at the 0.05-significance level, where the null hypothesis is The probability of a student passing the module is 0.75and the alternative hypoth- esis is The probability of a student passing the module is less than 0.75. What is the conclusion? [Hint: Clearly state any assumptions made and recall the conditions under which a bino- mial distribution can be approximated by a normal distribution.]
