``` name_____________________________________________________________version 1 QUESTION ONE [24] 1) Suppose you are given the chart below as a computer produced stem & leaf diagram of the GPA's of the set of students in some small program. Scale is given by the largest item which is 34. -0 | 99 +0 | 0011111112222222222222233333333333333334444 1 | 2 | 3 | 4 a) Cases where the GPA could not be calculated because not all grades were in were probably coded as ______________ b) What kind of error probably created the GPA of 34? . ______________________________________________________________________ . 2) To quadruple your precision you must mulitply your sample size by - 1.414 2 3 4 6 8 12 14 16 20 25 40 400 3) Rank these as as "BEST" "MIDDLE" and "WORST" according to suitability for describing with a standard deviation. * Distances flown by paper airplanes in assignment 7 __________ . * Heights of students now writing this exam. __________ . * Income of Canadian citizens __________ 4) A 9000 digit sequence from a base five random number generator is tested with a chi-square test. The generator is rejected when a chi-square statistic of 11.1 results. Which of these (more than one) are correct? a) The probability the generator is DEFECTIVE is 2.5% b) The probability the generator is GOOD is 2.5% c) The probability the generator is DEFECTIVE is 97.5% d) The probability the generator is DEFECTIVE is 5% e) The probability the generator is GOOD is 5% f) The probability the generator is DEFECTIVE is 95% g) For a GOOD generator Pr{chi-square > 11.1} = 0.025. h) For a DEFECTIVE generator Pr{chi-square > 11.1} = 0.025. i) For a GOOD generator Pr{chi-square > 11.1} = 0.975 j) For a GOOD generator Pr{chi-square > 11.1} = 0.05. k) For a DEFECTIVE generator Pr{chi-square > 11.1} = 0.05. l) For a GOOD generator Pr{chi-square > 11.1} = 0.95. m) Either the generator is DEFECTIVE or something unlikely has happened. n) Either the generator is GOOD or something unlikely has happened. 5) X and Y are independent random variables with variances of 74 and 30, respectively. Evaluate the variance of (X-Y+9). ____________ 6) A normal distribution has expectation 1000 and std. dev. 200. How much probability lies between -1150 and 1150? ___________``` ``` page 2 name_____________________________________________________________version 1 QUESTION TWO [20] Use the Minitab printout below in answering these questions Complete this table: X: 5 7 9 11 13 Y: 143 152 176 190 204 FIT: ____ ____ ____ ____ ____ RESIDUAL: ____ ____ ____ ____ ____ (7) ------- Identify the standard deviation of residuals on the Minitab printout by circling and labelling it Identify the sum of squares of residuals on the Minitab printout by circling and labelling it Calculate a 95% confidence interval for the slope _______ to _______ -------------------------------------------------- Selections from (simulated) Minitab output Data Display Row X Y 1 5 143 2 7 152 3 9 176 4 11 190 5 13 204 Regression Analysis The regression equation is Y = 101 + 8.00 X Predictor Coef Stdev Constant 101.000 5.447 X 8.0000 0.5774 s = 3.651 Analysis of Variance SOURCE DF SS MS Regression 1 2560.0 2560.00 Error 3 40.0 13.33 Total 4 2600.0 ``` ``` page 3 name__________________________________________________________version 1 QUESTION THREE [28] This question concerns the data of this stem & leaf diagram 1 | 1 4 2 2 | 2 2 2 3 | 1 3 5 3 Largest number is 78 4 | 2 1 5 | 0 6 | 1 4 5 3 7 | 0 2 7 8 4 Consider this as a random sample from some population. (a) Calculate the sample mean __________ (b) The standard deviation of this data is 24.02, from this estimate the standard deviation of the sample mean __________ (c) Calculate a 99% * NOT 95% * confidence interval for the mean _______ to _______ Among a class of 670, all calculating such a confidence interval from INDEPENDENT samples, what is the expected number of intervals which do NOT cover the population mean? __________ (d) Approximately how large a sample is needed to achieve a standard deviation of the sample mean equal to one instead of the value you calculated in (b) ? N = ___________ Use either of the tables handed out in class to determine a confidence interval for the median _______ to _______ Among a class of 670, all calculating such a median interval from INDEPENDENT samples, what is the expected number of intervals which do NOT cover the population median? __________``` ``` page 4 name_____________________________________________________________version 1 QUESTION FOUR [15] A die being tested for fairness is tossed 300 times with this result. FACE 1 2 3 4 5 6 COUNT 58 61 45 57 40 39 COUNT-50 8 11 -5 7 -10 -11 a) Calculate the chi-square statistic. b) Under the null hypothesis the probability of a value of chi-square as large or larger than (a) above is nearest 0.005 0.01 0.025 0.05 0.10 0.25 0.50 0.75 0.90 0.95 0.99 0.995 c) Suppose the die is really fair. In 100 such tests (A single test consists of tossing the die 300 times and calculating chi-square.) the expected number of times chi-square exceeds the valud you got above is closest to -- 0.5 1 2.5 5 10 25 50 75 90 95 99 99.5 QUESTION FIVE [ 5] In an experiment like the class paper airplane assignment, save that only one kind of airplane is used, each of ten people throw an airplane five times. The result can be presented as 50 sep- arate distances or as individual means for ANN, BOB, etc. Both presentations appear below. Average and standard deviation for each presentation is also shown. Thrower Data Mean ANN 39 36 50 44 49 43.6 BOB 65 71 63 67 70 67.2 CAL 37 36 23 38 38 34.4 DOT 35 48 45 49 41 43.6 EMMA 38 47 46 43 40 42.8 FAY 31 27 37 28 27 30.0 GAIL 42 44 48 48 49 46.2 HAL 60 51 63 55 69 59.6 IRA 41 43 48 40 51 44.6 JEAN 29 43 39 34 37 36.4 Average 44.84 44.84 Standard Dev. 11.69 11.19 Calculate a 95% confidence interval for the mean distance flown. 44.84 +/- ____________________________```

STAT 3093 - FINAL EXAM - 1997 AUGUST 9 - SOLUTION SHEET
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version 1
QUESTION ONE  [24]
1) Suppose you are given the chart below as a computer ......
a) ..................................................  -9
b)  ............................... MISSING DECIMAL POINT

3) Rank as as "BEST" "MIDDLE" and "WORST" for using std.
* Distances flown by paper airplanes in assignment 7     MIDDLE
* Heights of students now writing this exam.               BEST
* Income of Canadian citizens                             WORST

4) A 9000 digit sequence from a base 5 random # generator
g) For a GOOD generator Pr{chi-square > 11.1} = 0.025.
m) Either the generator is DEFECTIVE or something unlikely...
Grading:  NO ANSWER 1 :: (g)&(m) only 4  :: One right no wrong 3:
one right 1 wrong 2   :: two right 1 wrong 3

5) V{X}=74 V{Y}=30     Evaluate the variance of (X-Y+9).       104

6) How much probability lies between -1150 and 1150?        0.7734

QUESTION TWO  [20]
X:           5       7       9      11      13
Y:         143     152     176     190     204
FIT:       141     157     173     189     205
RESIDUAL:    2      -5       3       1      -1    [7]

Identify std of resid and SSQ of residuals [6]
Interval for B
8 +/- 3.182x 0.58  =  8 +/-  1.84 =  6.16 to  9.84  [7]
8 +/- 2.000x 0.58  =  8 +/-  1.15 =  6.85 to  9.15

QUESTION THREE [28]
Data:  11 14 22 22 31 33 35 42 61 64 65 70 72 77 78
Sample mean                                            46.47
Std of the sample mean                24.02/sqrt(15) =  6.20
Interval for MEAN     (30.5 62.4 Normal)        28.0 to 64.9
Expected misses (mean)                                  6.70
Required sample size                                     577
Interval for MEDIAN                       22-70   or   22-72
Expected misses (median)                  23.56         4.95

QUESTION FOUR  [15]
Chi-Square =   9.60    Upper Tail Probability 0.087

QUESTION FIVE  [ 5]
Without adjustment   Width = 2     * 11.19 / sqrt(10)  =    7.077
With adjustment      Width = 2.263 * 11.19 / sqrt(10)  =    8.008
>>> No credit if square root 50 is used.   ```