name _______________________________________________ version 1 FINAL EXAM - STATISTICS 3093 - 1996 DECEMBER OPEN BOOK -- NOTES & CALCULATORS ALLOWED -- TIME: 3 HOURS QUESTION ONE [24/80] 0 0 1 1 4 The largest number of this stem 2 2 8 and leaf diagram is 6.4 3 0 2 Calculate from this data the 4 0 4 7 quantities requested: 5 6 4 FIRST, SECOND & THIRD QUARTILES _______ _______ _______ MEAN (AVERAGE) ______________ STANDARD DEVIATION ______________ 95% CONFIDENCE INTERVALS FOR MEDIAN ____________ TO __________ FOR MEAN ____________ TO __________ QUESTION TWO [8/80] Each of a class of 16 is given a different block of digits from the same random number generator. All 16 test the generator using a chi-square test at alpha=0.10 ((NOT 0.05)) Assume all their work is correct. Even though the generator is OK some of the class will probably reject it. What is --- a) The expected number of rejections __________ b) The (small) probability that nobody rejects it __________ c) The probability that (exactly) one person rejects it. __________ QUESTION THREE [8/80] (A) Invent two sets of data: i) One OBVIOUSLY suitable for techniques using a standard deviation (such as confidence intervals for the mean). ii) One OBVIOUSLY NOT suitable for techniques using a std. dev. (B) Invent two scatter plots: i) One OBVIOUSLY suitable for regression (least squares) techniques. ii) One OBVIOUSLY NOT suitable for regression techniques.

page 2 stat 3093 name _______________________________________________ version 1 QUESTION FOUR [24/80] This table describes a simple linear regression (least squares fit). Fill in the missing numbers. Hint: Since two points determine a line, you can solve for the fitted line after finding any 2 points on it. After that, the rest is straightforward. X 1 2 3 4 5 Y 18 18 _____ 16 34 FITTED LINE _____ _____ _____ _____ 27 RESIDUAL 3 _____ -2 -8 7 Calculate the quantity which is an analog of the standard deviation describing the size of a "typical" residual. (Minitab reports this quantity as "s".) QUESTION FIVE [16/80] X is distributed as follows: P{X=1}= 0.3 , P{X=2}= 0.5 , P{X=3}= 0.2 Evaluate (as a number) the expectation and variance of 60/X X 1 2 3 Probability 0.3 0.5 0.2 60/X 60 30 20 Y is distributed the same way as X, and X and Y are independent. Evaluate (as a number) the expectation and variance of (a) 60/X + 30/Y _________ (b) 60/X + 30/X _________ ((Look carefully to see which are Y`s and which are X`s.))