6. Suppose a study examines the relative efficacy of penicillin and spectinomycin in treating gon- orrhea. Three treatments are considered: (1) penicillin, (2) spectinomycin, low dose, and (3) spectinomycin, high dose. Three possible responses are recorded: (1) positive smear, (2) nega- tive smear, positive culture, (3) negative smear, negative culture. The researchers want to see if there is an association between the type of treatment and the response. The data in Table below was obtained. Response Treatment + Smear - Smear, + Culture - Smear, - Culture Total Penicillin 40 30 130 200 spectinomycin, low dose 10 20 70 100 spectinomycin, high dose 15 40 45 100 Total 65 90 245 400 (a) We have discussed 3 different y tests: Goodness of Fit, Independence Test and Homogene- ity Test. Which test should you run for the information given and how do you know? (b) Get the data table into R as a matrix. Do not include the row and column totals. (c) Calculate the expected values for the observed values in the table. Do these pass the greater than 5 criteria for the expected values? (d) Is there an association between the type of treatment and the response? Perform the test you decided upon. Give me your hypotheses, test code and output, and a well written conclusion