Find the right test for the following problems. Also write down the null and the alternative hypotheses in each case. You do not need to actually do the test. Whenever necessary, assume that the population follows normal distribution. 

(a)  Investigators compared mean cholesterol level between cases (have heart disease) and controls (no heart disease). 57 cases and 62 controls were used. Which test would you use to answer the question if mean cholesterol levels differ by cases and controls?

(b)  The Department of Health conducted an observational study in which users of public restrooms at several sites were discreetly observed. Of the 634 females observed, 476 washed their hands. Of the 561 males observed, 326 washed their hands. What test should be used to determine whether these data provide sufficient evidence to reject the null hypothesis that the proportions of females that wash their hands when using a public restroom is the same as the proportion of males that wash their hands when using a public restroom?

(c)  A database contains high school and university grades for 105 computer science majors at a local state school. A college admissions advisor wants to know if SAT scores can be used to predict a student's university GPA. What test would you use to help answer this question?

(d)  In a study of breast feeding and IQ, 300 mothers decided if their infant should be fed by one of three methods: fed with her breast milk, fed with infant formula 1, or fed with infant formula 2.  At the age of 8 years, the IQ of the children was measured. What test should you use to test if there is any difference in the average IQ for the 3 different methods of feeding?