1. The following table shows the survival counts of the various classes on the Titanic. Survived Survived First Class Passenger E Second Class Passenger Third Class Passenger \" Total Passenger m We are interested in researching if there is any relationship between passenger class and the chance of survival in shipwrecks. Identify the null hypothesis. {4 Points) 2. 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 deciency. The superintendent fears that if it is not corrected, she will lose her job before long. As the superintendent was in her ofce 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 1mm 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 ,DDD,DDD. 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 1t] 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: |L'tuestlon 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) 3. A medical research team is investigating the benets of a new surgical treatment. One of the claims of this new surgical treatment is that the minimum recovery time for patients after the new treatment is less than 96 hours. How would you write the null and alternative hypotheses when you are on the research team (investigating the claims} and want to support the claim? How should you interpret a decision that rejects the null hypothesis? (Points = 4) 4. A survey asked how many colleges undergraduate students applied to, with 206 students responding to this question. This sample yielded an average of 9.? college applications with a standard deviation of 7. The College Board website states that counselors recommend students apply to roughly 3 colleges. How would you test if the data provide convincing evidence that the average number of colleges students apply to is higher than recommended? What would be your hypotheses? {Points = 4)