Chapter R, Problem 6.38RE

Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:

Hair Color	Eye Color
1 = Blond	1 = Blue
2 = Brown	2 = Green
3 = Black	3 = Brown
4 = Red	4 = Grey
5 = Other	5 = Other

The statistics students analyzing the data were asked to study the relationship between eye and hair color.

1. a) One group of students produced the output shown below. What kind of analysis is this? What are the null and alternative hypotheses? Is the analysis appropriate? If so, summarize the findings, being sure to include any assumptions you’ve made and/or limitations to the analysis. If it’s not an appropriate analysis, state explicitly why not.

Dependent variable is Eyes

R-squared = 3.7%

s = 1.112 with 1021 - 2 = 1019 degrees of freedom

1. b) A second group of students used the same data to produce the output shown below. The table displays counts and standardized residuals in each cell. What kind of analysis is this? What are the null and alternative hypotheses? Is the analysis appropriate? If so, summarize the findings, being sure to include any assumptions you’ve made and/or limitations to the analysis. If it’s not an appropriate analysis, state explicitly why not.

${\displaystyle \sum \frac{{(Obs-Exp)}^2}{Exp}}=223.6\text{P-value}<0.00001$