Problem 4 has been

- Agresti, Exercise 2.9
- Agresti, Exercise 2.12
- 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

- Calculate the conditional probabilities for wives' heights given husband's height.
- Compare the conditional distributions for tall, medium, and short men to one another. Are these distributions similar to one another?
- Calculate the four local odds ratios, as described in Agresti's equation (2.7), and arrange them in a two by two table.
- 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.

- 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.

*null hypothesis*.- What are the multinomial cell probabilities (pi's) for each type, if the null hypothesis is correct?
- What are the estimated frequencies (m-hat's) under this multinomial model?
- Calculate a chi-squared goodness-of-fit statistics to test the null hypothesis. What do you conclude?

- The textbook is on two-hour reserve in Eckhart library.