4. (15pt) A group of students were asked if they have ever driven after drinking. They also were asked, "How many days per month do you drink at least two beers?" In the following discussion, 7 = the probability a student says "yes" they have driven after drinking. This is modeled using X = number of days per month of drinking two beers using the model The estimated model is and s = 0.02946. logit() BoX logit () 1.5514 + 0.19031X (a) (5pt) Estimate of the probability of ever having driven under the influence when X = 4. (b) (5pt) Construct a 95% confidence interval for B and interpret your result (c) (5pt) Test Ho B = 0 against H B 0 using = 0.05. 5. (10pt) (Problem 4 continued) Next we will model the association between ever driven after drinking, X = days per month of drinking two beers adjusted for gender. The model is logit() BoX + BG where G = 1 if gender is male and G = 0 is gender is female. The estimated model is logit() -1.3104 +0.1055X+ 0.5301G (a) (5pt) Estimate the probability that a male ever drives after drinking when X = 4. (b) (5pt) If s = 0.4201, construct a 95% confidence interval for 2 and interpret your results.