A study was conducted in which rats showed compassion by freeing a trapped rat. In the study, all six of the six female rats showed compassion by freeing the trapped rat while 17 of the 24 male rats did so. We found a 95% confidence interval for the difference in proportion of rats showing compassion, using the proportion of female rats minus the proportion of male rats, to be 0.104 to 0.480. In testing whether there is a difference in these two proportions:

a. What are the null and alternative hypotheses?
b. Using the confidence interval, what is the conclusion of the test?
c. State the significance level used.
d. Based on this study would you say that female rats or male rats are more likely to show compassion (or are the results inconclusive)?

Which of the points a(6, 2), b(0, 0), c(3, 2), d(−12, 8), e(−12, −8) belong to the graph of direct variation y= 2/3 x?

Find the slope of the line passing through a pair of points

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? )