Question

Suppose Tom, an education researcher, wishes to determine the effects of mandatory study days prior to exams upon students in his state. Tom randomly selects 400 of the approximately 85,000 undergraduate students in his state and divides them into two groups of equal size. The first 200 students take a standardized chemistry examination and are graded as either passing or failing. The second 200 students take the same exam but participate in an exam study day immediately prior to the examination. Tom hopes that the designated study day will reduce the proportion of students who fail the examination. Students either receive a passing grade, P, or a failing grade, F, on the examination. This table shows the results of Tom's research.

Population	Population description	Sample size	Number of students earning an F	Sample proportion
1	No study day	n1=200	?1=58	?̂ 1=0.29
2	Study day	?2=200	?2=34	?̂ 2=0.17

Suppose Tom wishes to conduct a z‑confidence interval for the difference of two proportions to determine if the proportion of students who fail the exam is lower for students receiving a study day.

Which of the statements is true?

1)All of the requirements are met for Tom's z‑confidence interval.

2)Tom's z‑confidence interval is not valid because the sample was not taken using randomization.

3)Tom's z‑confidence interval is not valid because there are less than 10 successes and 10 failures in at least one of the groups.

4)Tom's z‑confidence interval is not valid because the two groups are not independent.

Answer 1

All of the requirements are met for Tom's z‑confidence interval.

Option 1 is correct.