A school newspaper article claims that 60% of the students at a large high school completed their assigned homework last week. Some skeptical AP Statistics students want to investigate this claim so they choose an SRS of 100 students from the school to interview. In their sample, 45 students completed their homework last week.

The sample proportion isp^= 0.45, which is less than 0.60. Which of the following statements must be false?

a)A sample proportion of 0.45 proves that less than 60% of the population of all students did their homework because 0.45 is less than 0.60.

b)Maybe the sample proportion is less than 60% because less than 60% of all students did their homework.

c)If 60% of the students completed their assigned homework last week then we would expect approximately 60 of the 100 students in the sample to respond "yes" to the question.

d)Maybe 60% of the students did their homework, but the students got a sample proportion less than 60% because of sampling variability.

e)The student used an appropriate sampling technique to collect these data.