RVS Analytics Practice Questions… Question - 1 A family has n >= 2 kids. All arrangement of the sexes of the children are equally likely. Let X be the event that the family has at most one girl. Let Y be the event that the family has children of both sexes . ( 15 Points ) • Find P(X) - 3 points • Find P(Y) – 4 points • Find P( X Y) – 3 points • Are X and Y independent – 5 points Question - 2 • Show that the mean is the best predictor when there is no other information available to predict Y - 5 points • Derive the equation of the slope parameter and the intercept parameter in the regression equation y = a + b(x) from the classroom discussion - 10 points Question - 3 A small business hires a consultant to predict the value of weekly sales of their product if their weekly advertising is increased to $750 per week. The consultant takes a record of how much the firm spent on advertising per week and the corresponding weekly sales over the past six months. The consultant writes ‘‘Over the past six months the average weekly expenditure on advertising has been $500 and average weekly sales have been $10,000. Based on the results of a simple linear regression, I predict sales will be $12,000 if $750 per week is spent on advertising.’’ - 5 points What is the estimated simple regression used by the consultant to make this prediction? Question - 4 You are an analytics expert and hired by the Equal Employment Opportunities Commission to provide judgement in a case registered against the HR head of Heldi Ltd. by Dheela Shikshit , an analytics manager recruited recently by Kevin Arjiwal , the HR head of Heldi Ltd. Dheela claims that Kevin pays men higher salaries than women. Explain how you would use statistics (analytics techniques learnt in the class) to take the right judgment. – 25 points • Mathematical Construct – Equation and Justification of Equation - 10 points • What points will you consider before taking the decision – 5 points • Identifying potential pit falls in your judgement – 10 points
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