STAT 207. ASSIGNMENT NO. 3

Due on Tuesday, Sept 22, 1998

Read Chapters 4-5.

Do the following problems:

4.7. Also compute the 5% trimmed mean.

4.21 and 4.22. Also compute the corresponding coefficient of variation for each case.

4.30.

4.54. Use the additional information provided below to complete a, b, c, where the data set and their sorted values are:

         
            1      2     3      4      5     6     7      8      9    10 
Stocks     1.66  32.54 -7.52  15.56  25.30  6.54 -7.10  18.00  22.36 -0.96
Bonds.     7.10   9.78  3.05   4.60   6.59  0.96  1.55  -2.20  -0.52 -2.31
S.Stocks -26.61 -10.29 -7.52  -7.10  -3.60 -2.44 -0.96  -0.42   1.66  5.51
S.Bonds. -21.98  -3.02 -2.62  -2.31  -2.20 -1.69 -0.52   0.45   0.96  1.11

             11    12    13    14     15    16    17    18    19     20    
Stocks     -3.60  8.07 27.31 -0.42 -26.61 19.70 10.94  9.93 29.22  44.38 
Bonds.    -21.98 11.55  1.11  1.71  -1.69  2.82 19.02  5.97  1.29  -2.62 
S.Stocks    5.88  6.54  8.07  8.95   9.93 10.94 11.08 15.56 18.00  19.70 
S.Bonds.    1.29  1.55  1.71  2.06   2.82  3.05  4.60  5.97  6.59   7.10 

           21     22    23    24     25    26    27    28    29    30 
Stocks    29.93 -10.29  5.51 34.84  -2.44 25.07  8.95  5.88 11.08 21.37
Bonds.     2.06  -3.02 42.98  9.60  15.09 25.26 17.54  0.45 10.45 16.29
S.Stocks  21.37  22.36 25.07 25.30  27.31 29.22 29.93 32.54 34.84 44.38
S.Bonds.   9.60   9.78 10.45 11.55  15.09 16.29 17.54 19.02 25.26 42.98
with S.Stocks being the sorted values of Stocks and S.Bonds being the sorted values of Bonds. Some simple summary statistics are:
      
       Stocks                   Bonds.        
 Min.   :-26.61            Min.   :-21.9800  
 1st Qu.: -0.42 (0.10*)    1st Qu.:  0.45   (0.5775*)
 Median : 10.43            Median :  2.9350  
 Mean   : 11.84            Mean   :  6.0830  
 3rd Qu.: 25.07 (24.39*)   3rd Qu.: 10.45   (10.2800*)  
 Max.   : 44.38            Max.   : 42.9800

(The values marked by * are those produced by my computer package, which uses a slightly different rule of computing the "exact" percentiles. You can use either value (e.g. 25.07 or 24.39) to build your boxplots, but must be consistent in using these values, i.e. either all from the computer output or ...)

4.55.

4.58. ( tex2html_wrap_inline41 .)

Exercise A1: There is a definition of simple random sampling in the text. What is the other one we gave today in the lecture?

Exercise A2: A 1989 salary survey (Working Woman, January 1989) listed the average salary of elementary and secondary school teachers as $28,085. Assume that the standard deviation of salaries is $4500.

a. Janice Herbranson was identified as a teacher in a one-room schoolhouse in McLeod, North Dakota. Her salary was reported to be $8100 per year. What is the z-score associated with $8100? Comment on whether this salary figure is an outlier.

b. Compute the z-score for each of the following salaries: $33,500, $25,200, $28,985 and $39,000. Should any of these be reviewed as possible outliers?

(Hint: Based on the empirical rule, the values that are out of 3 standard deviation of the mean are candidate outliers.)

Exercise A3: Use the salary data in Exercise A2 and Chebyshev's theorem to find the percentage of elementary school teachers that must have salaries in the following ranges: a. $19,085 to $37,085; b. $14,585 to $41,585; c. $14,585 to $42,000; d. Repeat parts (a) and (b) if it can be assumed that the distribution of teacher salaries is approximately bell-shaped.



Sept 15, 1998