Starter cultures containing a mixture of lactic acid bacteria (namely, Lactococcus lactis, Lactococcus cremoris, and Streptococcus thermophilus) were diluted in the proportion of 1:100, and inoculated in petri dishes containing non-selective agar (agar is a gelatinous substance used as a growing medium for bacteria). Immediately after inoculation, the antibiotics penicillin and/or tetracycline were introduced into the petri dishes in various concentrations (except for the control group). Treatments were randomly assigned to the 24 petri dishes, one treatment per dish. Treatment Antibiotic/Concentration Control (no antibiotics) Penicillin 0.05 ppm (parts per million) Tetracycline 0.05 ppm Penicillin 0.075 ppm Tetracycline 0.075 ppm Both Penicillin 0.05 ppm and Tetracycline 0.05 ppm 2 3 4 5 6 48 hours after inoculation, bacterial growth in each petri dish was measured in Colony Forming Units per milliliter (CFU/ml). Treatment Bacterial Growth (CFU/ml) 267 263 266 260 83 87 82 80 88 77 80 84 82 65 68 66 70 62 56 59 5 35 38 36 40 123 4S6 (fi) The research or alternate hypothesis is that the combination of penicillin and tetracycline (i.e. penicillin and tetracycline together) decreases expected bacterial growth by more than 30 CFU/ml compared to both expected bacterial growth for tetracycline alone and expected bacterial growth for penicillin alone (together). Note: only one linear combination is called for here. Set up the null and alternate hypotheses in terms of the appropriate linear combination of the population means. HA: Calculate the P-value. Do you accept or reject the null hypothesis? Why? Base your decision to accept or reject the null on the P-value only. (f ii) Using the appropriate confidence interval only, perform the hypothesis test of (fi) with P(I) = 0.05. Do you accept or reject the null hypothesis? Why? (f i) Interpret the confidence interval that you constructed in part (f ii) within the context of this experiment. Note: the interpretation of this confidence interval has absolutely nothing to do with the hypothesis test. Disregard the hypothesis test completely when answering this part.