A bacteriologist is interested in the effects of two different culture media and two different times on the growth of a particular virus. She performs six replicates of a 22 design, making the runs in random order. Analyze the bacterial growth data that follow and draw appropriate conclusions. Analyze the residuals and comment on the model's adequacy. Culture Medium Time 12 Hr 18 Hr 1 21 23 20 37 38 35 2 22 28 26 39 38 36 25 24 29 31 29 30 26 25 27 34 33 35 a. By hand calculation, use the simplified calculation method described in the PowerPoint materials to calculate the effects and confidence intervals to determine which effects are significant. b. Using the matrix algebra approach described in the PowerPoint materials, calculate the effects, create an ANOVA table, interpret your results and make recommendations. c. Write down a regression model for predicting vibration based on the results of this experiment. Based on the analysis, what coded factor levels would you recommend using? d. Confirm your answers above using Minitab; create cube plots, interaction plots, residuals plots, and any other graphics which support your analysis