Chapter PVII, Problem 17RE

(a)

To determine

To explain what kind of analysis is this and what are the null and alternative hypotheses and also explain is the analysis appropriate or not.

Answer to Problem 17RE

This is regression analysis.

Explanation of Solution

It is given in the question that a survey of $1021$ school age children was conducted by randomly selecting children from several large urban elementary schools. One group of students produced the output shown in the question. Thus, by looking at the computer output, we can say that this is a regression analysis of Eye colour on Hair colour. The variables are of categorical. The variables are not quantitative variables. Here regression is not an appropriate analysis. The scatterplot given in the question clearly indicates that there is inexistence of regression analysis.

(b)

To determine

To explain what kind of analysis is this and what are the null and alternative hypotheses ad explain is the analysis appropriate.

Answer to Problem 17RE

This is a two-way table that is appropriate. The null and alternative hypotheses are as:Null hypothesis: Eye and Hair colour are independent. And Alternative hypothesis: Eye and Hair colour are independent.

Explanation of Solution

It is given in the question that a survey of $1021$ school age children was conducted by randomly selecting children from several large urban elementary schools. A second group of students used the same data to produce the output shown in the question. The table is displays the counts and standardized residuals in each cell. We have,

  $\begin{array}{l}{\chi }^2=223.6\\ df=16\\ P<0.00001\end{array}$

Now, by looking at the table we can say that it is a two-way table that is appropriate. The null and alternative hypotheses are as:

Null hypothesis: Eye and Hair colour are independent.

Alternative hypothesis: Eye and Hair colour are independent.

However, four cells have expected counts less than five, so the chi-square analysis is not valid unless cells are merged. However, the results are not likely to change if we merge appropriate eye colours.