Unformatted text preview: e ACT score. Let X be the SAT score for a student and Y be the corresponding ACT score. a. (4 points) If the observed correlation between X and Y is found to be 0.8 then what must be the covariance between X and Y? SXY
SX S Y
SXY = rXY SXS Y = 0.8(4)(200) = 640 rXY = b. (4 points) What are the units of the covariance? ACT Units * SAT Units c. (4 points) Suppose we wanted both scores to be as a percentage of the perfect scores in each test. What transformations would we need to apply to achieve this for each variable? W =100*(1/2400)*X = (1/24)*X ‐‐ SAT as % Z =100* (1/36)*Y – ACT as % d. (4 points) Find the mean and variances of the transformed variables. Means: 2200/24 = 91.7 and (100)33/36 =91.7– no need to compute Variances: (1/24)2 *(200)2 = 69.4 and (100/36)2*(4)2 = 123.4 no need to compute e. (4 points) Find the covariance and correlation between the transformed variables. Cov = (100/2400)*(100/36)*640 = 74.07 Correlation = 0.8 In c,d,e students may have not multiplied by 100 and used a percentage expressed as a proportion – give full credit if answers are consistent with that. 3. (12 total) Professor Donald has a collection of heavy metal songs on his ipod. He has 20 songs by Metallica, 15 songs by Megadeth and 10 songs by Black Sabbath. He decides to play his ipod in shuffle mode whereby songs are randomly selected from his collection. Professor Donald only has time to listen to 6 songs. For the following you just need to write down the appropriate formula and you do not have to do the numerical calculation. a. (3 points) If there are no repeats how many different combinations of songs are possible? 45 C6 b. (3 points) If there are no repeats then how many different sequences of songs would be possible? 45 P6 = 45 C6 •6 P6 c. (3 points) How would your answers to the previous parts change if repeats were possible? For this just state ``increase’’, ``’’decrease’’ or ``unaff...
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- Spring '08