Psychologist Alison Gopnik discusses two prominent modes of parenting in modern America: the gardener and the carpenter. Whereas carpenter parents try to actively shape their children into particular kinds of people, gardeners concentrate on providing environments and resources that will support the direction of their children’s development regardless of the particular direction.

A researcher develops a scale that measures parents’ carpenter and gardening tendencies, where 1 means an exclusive carpenter orientation, 2 means a mix of carpenter and gardener, and 3 means an exclusive gardener orientation. He wants to know whether this parenting approach is related to children’s anxiety.

Table 12.24 shows the cross-tabulation of parenting approaches and children’s anxiety in a sample of 200 children.

a. What are the null and alternative hypotheses for a chi-square test of independence?

What does the null hypothesis say about the distributions of anxiety levels for each parenting style compared to the others in the population?

b. What are the degrees of freedom and decision chi-square for this test, assuming a 0.025 alpha-level?

c. The sample chi-square is 14.7. Should the null hypothesis be rejected?