1. A bacteriologist is studying the antibiotic properties of four solutions (labeled T1 through T4 in the dataset antibiotics on Canvas). The bacteriologist measures the reduction in bacterial cultures when each solution is applied and would like to know which solutions are more effective than others as antibiotics.
a. Examine the data by making a side-by-side boxplot for the reduction in bacterial cultures for each treatment group (refer to the Homework 2 Guide for a refresher on making box plots).
b. What are the null and alternative models for an ANOVA in this context?
c. Evaluate the assumptions for ANOVA (refer to the Lecture 11a Prereading and the Homework 2 Guide for reminders about the relevant R code).
d. What is the value of the test statistic for an ANOVA of the antibiotic data? What does this test statistic represent, in the context of the scenario? Name two conditions that, if changed, would result in a smaller test statistic.
e. Explain what conclusion the bacteriologist should draw, based on the data.
f. Find Tukey-adjusted 95 percent confidence intervals for the difference in each pair of solutions. Which solutions are significantly different from the others?
g. Would the unadjusted confidence intervals be wider or narrower? Explain
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