Question: Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. In the sample, 27 students said "No." The Fathom dotplot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the water off is 0.50.
(a) Explain why the sample result does not give convincing evidence that fewer than half of the school's students brush their teeth with the water off.
(b) Suppose instead that 18 students in the class's sample had said "No." Explain why this result would give strong evidence that fewer than 50% of the school's students brush their teeth with the water off.