1. We return to the survey of 34 patients having surgery with a general anesthetic. Patients were asked whether or not they experienced a sore throat (throat=0 for no, throat=1 for yes). The duration of the surgery in minutes was also recorded. (a) Refit (or return to) the simple linear logistic regression model fit to this data in HW 2. Use the anova function to summarize the model, and use the ANOVA table to formally test at level = 0.05 whether including surgery duration as a predictor results in a better model than using an intercept alone. Make sure to specify the hypotheses, the test statistic, the distribution of the statistic under the null, the p-value, and your conclusion. (b) Predict the probability of a randomly chosen patient who has surgery having a sore throat when the duration of surgery lasts 30 minutes, and produce a 95% CI for this quantity. (c) Suppose that half the patients in the study were taken from one hospital and the other half were taken from another hospital. Would you be concerned about the inference that you carried out in part (b)? Explain your reasoning.