Question: A professor planned to give an examination in a large class on the Monday before Thanksgiving vacation. Some students asked whether he could change the date because so many of their classmates had at least one other exam on that date. They speculated that at least 40% of the class had this problem. The professor agreed to poll the class, and if there was convincing evidence that the proportion with at least one other exam on that date was greater than .40, he would change the date. Of the 250 students in the class, 109 reported that they had another exam on that date.
a. What proportion of the class reported that they had another exam on that date?
b. Is the proportion you found in part (a) a sample proportion or a population proportion?
c. The professor conducted a z-test of H0: p = .40 versus Ha: p > .40 and found z = 1.16 and p-value = .123. He said that he would not move the exam because the null hypothesis cannot be rejected, and there is not convincing evidence that the population proportion is greater than .40. What is wrong with his reasoning? [Hint: Refer to part (b).]