1. the day after surgery, 5 subjects get physical therapy 3 times a day for a week. another 5 subjects do not get physical therapy. the data are the number of days between the day of the surgery and the day on which the subject returns to work. treatment group: 12, 11, 14, 12, 12 nontreatment group: 15, 14, 17, 18, 17 (a) what is the mean for each group? what is the difference in the means? (b) randomly pick any 5 values from a mixture of both groups. find the mean of each group and the difference. repeat this process 4 times. (c) based on your differences of the means from being randomly picked, is the difference in means of the treatment group and nontreatment group significant? what does it mean?

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )