A superintendent in a medium size school has a problem. The mathematical scores on nationally standardized achievement tests such as the SAT and ACT of the students attending her school are lower than the national average. The school board members are greatly concerned about this deficiency. The superintendent fears that if it is not corrected, she will lose her job before long.

As the superintendent was in her office wondering what to do, a salesperson approached to offer the superintendent a "deal she couldn't refuse." The deal was teaching machines to teach mathematics, guaranteed to increase the mathematics scores of the students.

The salesperson informed, since there were about 1000 students in the school and one machine was needed for every 10 students, the school would need about one hundred machines. At a cost of $10,000 per machine, the total cost to the school would be about $1,000,000. The superintendent was not sure if the school board would go for such a big expenditure. The salesperson was prepared with an offer to lease 10 machines for testing purposes to the school for one year at a cost of $500 each was made. At the end of a year the superintendent would make a decision about the effectiveness of the machines. If they worked, she would pitch them to the school board; if not, then she would return the machines with no further obligation.

An experimental design was agreed upon. One hundred students would be randomly selected from the student population and taught using the machines for one year. At the end of the year, the mean mathematics scores of those students would be compared to the mean scores of the students who did not use the machine. If the means were different enough, the machines would be purchased.

Section II: Question

a. What is the null hypothesis? (Points = 3)

b. What is the alternative hypothesis? (Points = 3)

c. What are the two possible realities (states of the world) regarding the machines' effectiveness? (Points = 2)