R Assignment 3 Use statistics and R to answer the following questions. Make sure your answers are complete. - Answer each question and provide an explanation to support your answer. - Provide the R commands you used. - Provide Plots if applicable. Use appropriate and clear labels for the x and y axes and give a title for the plot. - Save your answers as a PDF file and name it using this format: Lastname Firstname R3 (No commas, dashes or other symbols). The accompanying dataset (HW3 datafile.csv) consists of observations on shower-flow rate (L/min) for a sample of 129 houses in Perth, Australia. A city commissioner claims that the average shower-flow rate is 8.3 L/min. Use the dataset to answer the following questions: a) What is a typical, or representative, flow rate? b) Construct a boxplot of the data and comment on interesting features. (Hint: Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry? Would you describe any observation as being far from the rest of the data (an outlier)? If so, list these values). c) Construct a normal probability plot. Is it plausible that shower-flow rate is normally distributed? Is a normal distribution assumption needed in order to calculate a confidence interval for the true average flow rate using the data? Explain. d) Calculate and interpret a 95% confidence interval for the average shower-flow rate. (Follow the approach and formulas presented in this class). e) Conduct a hypothesis test at the 0.05 significance level to test the commissioner's claim. Your answer must include the null and alternative hypotheses, test statistic, p-value, and a conclusion in the context of this dataset. (Follow the approach and formulas presented in this class).

Rate 4.6 12.3 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1 11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5 7.5 6.2 5.8 2.3 3.4 10.4 9.8 6.6 3.7 6.4 8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.8 6.2 5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3 7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.9 7.2 5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2 8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7 5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6 10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6 7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3 9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2 8.3 3.2 4.9 5.0 6.0 8.2 6.3 3.8 6.0