Diagnostic testing to identify and guide treatment of acute bacterial prostatitis is best accomplished by obtaining which of the following?  

_____ is a congenital abnormality characterized by the urethral opening located on the ventral (underside) surface of the penis, often associated with a ventral curvature of the shaft (chordee).

A 3-year-old girl with a history of recurrent febrile urinary tract infections is found to have vesicoureteral reflux (VUR) on voiding cystourethrogram (VCUG). She is currently asymptomatic. What is the most appropriate first step in management?  

A 45-year-old patient presents with chronic crusting and redness of the eyelid margins, associated with itching and burning. Visual acuity is normal. On exam, there is mild conjunctival injection and scaling at the lid margins. What is the first-line management?

A patient presents with a painless, firm nodule on the upper eyelid that has been present for 6 weeks. The lesion is not tender, and there are no signs of infection. What is the most appropriate initial management?

A 3-year-old girl is brought to the clinic by her mother, who reports noticing a firm “lump” on the child’s left side during bath time. The child has no fever, pain, or changes in appetite. There is no history of recent trauma. On physical examination, you palpate a firm, smooth, non-tender mass in the left upper quadrant that does not cross the midline. Vital signs are stable, and there are no signs of acute illness. What is the most appropriate next step in management?

Consider a market with only one firm operating in it, which we identify as the leader (L) firm. There is, however, a second firm evaluating whether or not to enter the market. We shall identify this firm as the entrant (E).  Cost functions are given by and , where is the fixed entry cost that the entrant must pay to start producing. Market demand is given by  where (of course, if the entrant is not in the market, then ).  As in the Stackelberg environment, competition takes place in two stages: in the first stage, the leader chooses its quantity, and in the second stage, the entrant observes the leader’s quantity and decides whether to enter or not. If it does, the entrant chooses how much to produce at the same time. Hint: Price and quantity are integers.  a)  (7 points) Find an expression for the entrant’s reaction(best response) function. b) (12 points) Assuming , will the entrant enter? Explain whether the market is a duopoly or a monopoly. Derive the two firms’ quantities and profits. Still, . The government desires the entrant to enter the market. So, the government chooses to support the fixed cost () of the entrant to remove the entry barrier. c) (2 points) Which value of should government at most aim for? In otherwords, how much makes the entrant’s profit indifferent between enteringand not entering? The government starts to support for the new firms. Now,  for the entrant. d) (6 points) Now consider the strategies that the leader can choose. Derive the quantity and profit of the leader’s firm and the entrant’s firm.

A nutritionist wants to see whether a new diet will help reduce weight for women. He randomly selects 15 women and assigns them to the new diet program (the length of the program is one month). For each woman, he records their weights as they start the diet and after they complete the diet program. To test whether the mean reduction in weight is significant, we would do:

Suppose we want to estimate the population proportion p within 2% (i.e. margin of error is 2%) with confidence level of 90%. What sample size do we need to ensure this? Choose the appropriate z-multiplier for the calculation from the following values: 

Please note that this question consists of four parts. You may use MINITAB to double check your final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. Researchers are interested in testing whether there is any difference between the proportions of adult patients who still had hives 30 minutes after taking medications A and B. Formulate the appropriate null and alternative hypotheses that answer the research question (in terms of the appropriate parameter(s)).  What conditions need to be satisfied for the hypothesis test in part 1? Are they satisfied? In addition to stating whether the conditions are satisfied or not, state and check the conditions.  Calculate the test statistic and the p value for the test in part 1. Show all your work. (Using MINITAB is not acceptable.) State the final conclusion of the test at 5% significance level in the context of the problem.