1. A researcher hypothesizes that the average number of sports that colleges offer for males (Population 1) is greater than the average number of sports that colleges offer to females (Population 2). A random sample of 50 colleges is selected with Y, = 8.6 and s, = 3.3 and X, =7.9 and s, =3.2. At a = 0.10 , is there enough evidence to support the claim? Calculate the p-value for this test. 10 marks 2. Using the information from Question 1, construct a 98% confidence interval for the true difference in average number of sports that colleges offer for males and for females. 6 marks 3. A researcher wishes to try three different techniques for lowering blood pressure of individuals diagnosed with high blood pressure. The subjects are randomly assigned to three groups; the first group takes medication, the second group exercises and the third group follows a special diet. After four weeks, the reduction in each person's blood pressure is recorded. The data is shown below: Medication Exercise Diet 10 6 5 12 8 9 12 Wi 15 8 13 2 4 At a = 0.05, test the claim that there is a difference between the three techniques for lowering blood pressure