A report released by the College Board asserted the percentage of students who took and passed Advanced Placement (AP) courses in all subjects has increased in every state and the District of Columbia since 2000. Among public school students, 14.1% earned a passing grade on at least one AP exam, the report indicated. In an attempt to determine if the proportion of those passing the math and science AP exams is equal to the 14.1% success rate, a random sample of 300 students enrolled in AP math and science classes has been selected.
a. If 35 of the students in the sample passed at least one AP math or science exam, calculate the proportion of those students who passed at least one AP math or science exam. Does this statistic indicate that the proportion of students who pass at least one AP math or science exam is less than that of those taking AP exams as a whole? Support your assertions.
b. Calculate the probability that a sample proportion equal to or less than that calculated in part a would occur if the population proportion was actually 0.141. Answer the question posed in part a using this probability.
c. Calculate a 98% confidence interval for the proportion of those students who passed at least one AP math or science exam. Answer the question posed in part a using this confidence interval. Does this answer correspond to that of part b? Support your assertions.