A professor was concerned that her students were not doing as well on the second exam of the semester as they did on the first exam. She used a random number generator to select a sample of 40 students from the 480 students who had taken this class in the last five years. She looked at the scores and identified that of the 40 students, 29 had received a grade of B or higher on the first exam, while 22 of the 40 students received a grade of B or higher on the second exam. The professor then proposed calculating a two-sample z-interval for p1 – p2, where p1 is the proportion of students receiving grades of B or higher on the first exam, and p2 is the proportion of students receiving grades of B or higher on the second exam. Are the conditions met for such a confidence interval? No, the two samples are not independent.
No, the sample was not a random sample.
No, there are not at least 10 scores below B in each of the samples.
No, there are not at least 10 scores above B in each of the samples.
Yes, there are no violations, so a two-sample z-interval for the difference in proportions is appropriate.