Stella saw the following headline in a national newspaper: “30 Percent of High School Students Favor Extended School Day.” She wondered if the percentage of students at her school who favor an extended school day was less than 30 percent. To investigate, she selected a random sample of 50 students from the 1,200 students at her school and asked each student in the sample if he or she favors an extended school day.

Only 12 of the students in the sample favored an extended school day. Because the sample percentage is (12/50)100 = 24%, Stella thinks that fewer than 30 percent of the students at her school favor an extended school day. She wonders if it would be surprising to see a sample percentage of 24 or less if the school percentage is

really 30.

(a) To see what values of the sample percentage would be expected if the school percentage was 30, she decides to use 1,200 beads to represent the population of 1,200 students. She will use a red bead to represent a student who favors an extended school day and a white bead to represent a student who does not. How many red beads and how many white beads should Stella use?

Stella put all the beads in a box. After mixing the beads, she selected 50 of them and computed the percentage of red beads. She put the 50 beads back in the box and repeated this process 99 more times. Then, she made the following dotplot of the 100 sample percentages:

(b) If the school percentage were actually 30%, how surprising would it be to see a sample percentage of 24% or less? Justify your answer using the dotplot.

(c) Based on her sample data, should Stella conclude that the percentage of students at the school who favor an extended school day is less than 30%? Explain why or why not.