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Unformatted text preview: Stat 104 Spring 2011 Final Exam Review Session Solutions 1. The following are a collection of unrelated quick problems. Briefly justify your answer for each problem. a) Suppose that A and B are two disjoint events within the same sample space. In addition, let P(A) = 1/8 and P(B) = 1/4. Are events A and B independent? Explain. They are dependent. Since A and B are disjoint, this means there is no intersection: P(A and B) = 0. Thus P(A)*P(B) P(A and B) [1/32 0]. b) Suppose a particular outcome from a random event has a probability of 0.02. Which of the following statements represent correct interpretations of this probability? Circle the right answer and provide justification. i) The outcome will never happen. ii) The outcome will happen two times out of every 100 trials, for certain. iii) The outcome will happen two times out of every 100 trials, on the average. iv) The outcome could happen, or it couldn't, the chances of either result are the same. Option (iii) is correct. There is a chance that 1/100 trials will have the outcome happen, or 3 out of 100, etc... but in the long run we would expect 2 successes out of 100 trials. c) If females of a certain species of lizard always mate with males that are 0.75 years younger than they are, what would the correlation coefficient between the ages of these male and female lizards be? Circle the right answer and provide justification. i) 0.75 iv) 1 ii) -0.75 v) -1 iii) vi) Not enough information to tell Option (iv) is correct. Since this is a deterministic relationship (meaning: male lizard ALWAYS are 0.75 years younger than their female mates), then the points lie exactly along the line, so the correlation is perfect: exactly 1 (draw the scatterplot to convince yourself). d) Consider the annual salaries of mutual fund managers in the Boston area. The mean salary is $450,000 and the median salary is $380,000. Circle the correct answer below. The probability that the salary of a randomly selected mutual fund manager from the Boston area is larger than the mean of $450,000 is: i) > 0.5 iii) = 0.5 ii) < 0.5 iv) Cannot be determined Option (ii) is correct. Since the mean > median, this implies its right skewed. We know 50% of the data is to the right of the median, and since the mean is larger, less than 50% must be to the right of it. (Draw a distribution that is right-skewed to convince yourself). 2. While sitting outside the Science Center and eavesdropping on cell phone calls for his project, a stat 100 student finds that only 11 of 27 men use a curse word during their conversations, while 24 of 33 women do. (a) Calculate the 95% CI for the difference in proportions of using curse words on the phone for women vs. men....
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- Fall '11