a) Distinguish between Regression and Correlation giving the differing scenarios of their usage in statistical analysis. [10 marks] b) The Educational Testing Service conducted a study to investigate the difference between the scores of male and female students on the Scholastic Aptitude Test. The study identified a random sample of 562 female and 852 male students who had achieved the same high score on the mathematics portion of the test. That is, the female and male students were viewed as having similarly high abilities in mathematics. The verbal scores for the two samples are as given: Female students: W1 = 547 and $1 = 83 ; Male students: W2 = 525 and $2 = 78 Do the data support the conclusion that given a population of female students and a population of male students with similarly high mathematics abilities, the female students will have a significantly higher verbal ability? Test at a 5% level of significance. What is your conclusion? [5 marks] c) The output of two workers was compared over a number of days with the following results: Average output Standard Number of days per day deviation Observed Man A 28 5 50 Man B 33 5 60 life