Homework Set 2

Due Thursday, January 23, 1997

Last updated 19-Jan-97 15:03
Problem 4 has been

  1. Agresti, Exercise 2.9

  2. Agresti, Exercise 2.12

  3. Booth's data on marriage-partner selection from Galton (18--) are reproduced below, with rows and columns arranged in a more customary order, that is, the column order (right to left) is the same as the row order (top to bottom). 
               | Husbands                                   
  Wives    |       Tall       Med      Short |     Total
-----------+---------------------------------+----------
      Tall |        18         20         12 |        50
       Med |        28         51         25 |       104
     Short |        14         28          9 |        51
-----------+---------------------------------+----------
     Total |        60         99         46 |       205
    1. Calculate the conditional probabilities for wives' heights given husband's height.
    2. Compare the conditional distributions for tall, medium, and short men to one another. Are these distributions similar to one another?
    3. Calculate the four local odds ratios, as described in Agresti's equation (2.7), and arrange them in a two by two table.
    4. You hypothesize that in the particular culture from which the data above were taken, men tend to select wives, that taller wives are generally considered more desirable by the men, and that men of medium stature are less able than tall or short men to select desirable mates. Construct an appropriate contingency table that would permit you to examine this hypothesis.

  4. In a series of plant genetics studies, Lindstrom (1918) crossed two varieties of maize. The second generation of plants produced four different phenotypes: green, golden, green-striped, and golden-green-striped. Of 1301 plants in this generation, the distribtution among phenotypes was: 
      "type"  count  description           
  ------ ------- --------------------- 
    1      773   green                 
    2      231   golden                
    3      238   green-striped         
    4       59   golden green-striped  
          ----                         
          1301                         

NOTE: An earlier version had 779 instead of 773 for the green count;
The version above has been corrected.
    A simple Mendelian inheritance model for these two traits would predict these combinations in the ratio of 9:3:3:1. This scenario will be our null hypothesis.
    1. What are the multinomial cell probabilities (pi's) for each type, if the null hypothesis is correct?
    2. What are the estimated frequencies (m-hat's) under this multinomial model?
    3. Calculate a chi-squared goodness-of-fit statistics to test the null hypothesis. What do you conclude?

Notes