2. [20 pts] You are testing the efficacy of an exercise-based weight loss intervention. A secondary aim of the study is to investigate whether the success of the intervention is affected by the level of dietary fat that the individual consumes. A subset of 11 participants are chosen and followed over the study period, leading to the following results: High-Fat Diet Low-Fat Diet Success 1 2 Failure 4 4 Did fat content in the diet play a role in the success of the intervention (SEE TABLES BELOW that may be useful for answering this question)? 2a) [10 pts] Test this hypothesis using a two tailed Fisher's exact test. Write the hypotheses and report the p-value for the test (SEE tables below for the probability of observing each possible table). 2b) [10 pts] At a significance level a = 0.1, in the context of the problem interpret the results of your test. 0 HF LF 1 HF LF Success 0 3 3 Success 1 2 3 Failure 5 3 8 Failure 4 4 8 5 6 5 6 Probability 0.1212 Probability 0.454545 2 HF LF 3 HF LF Success 2 1 3 Success 3 0 3 Failure 3 5 8 Failure 2 6 8 5 6 5 6 Probability 0.363636 Probability 0.060606 G GE lil A A 5. [20 pts] Researchers are interested in factors affecting young women's completion of the recommended 3 shot regimen of guardasil within 12 months of receiving the first shot. They collected the following information: Completed-completion status of the regimen (1 if completed all 3 shots within 1 year of the first, or 0 otherwise) Age the patient's age in years Race the patient's race (0 = white, 1 = black, 2 = Hispanic, 3 = other/unknown) LocationType = was the clinic in a suburban or an urban location (0 = suburban, 1 = urban) Assuming that the assumptions of logistic regression hold for this data set, answer the following questions using the following output: logistic completed age i. race locationtype Logistic regression Log likelihood = -874.10333 completed age Number LR chi2 (5) Prob chi2 Pseudo R2 of obs 1,413 47.80 0.0000 0.0266 Odds Ratio Std. Err. Z P>|z| [95% Conf. Interval] .9621625 .0135101 -2.75 0.006 .9360443 .9890095 race 1 .5249744 .0722998 -4.68 0.000 .4007838 2 .8812519 .2731589 -0.41 0.683 .4800161 3 .8267543 .1430699 -1.10 0.272 .5889467 .687648 1.617873 1.160585 locationtype cons .5873357 .0796174 1.473123 .4186401 -3.93 0.000 1.36 0.173 .4502981 .7660774 .8439948 2.571213 Note: _cons estimates baseline odds. 5a) [10 points] Is the overall logistic regression model significant? Answer yes or no, and write the test statistic and p-value. (no need to interpret the overall model for this answer) 5b) [10 points] How would you interpret the effect of location type on completion of the regimen? In your interpretation, discuss the significance of location type (include the p-value), interpret what the value in the "odds ratio" column means, and include and interpret the 95% confidence interval. Normal