Chang, Sandhofer, and Brown (2011) wondered whether mothers used number words more, on average, with their preschool sons than with their preschool daughters. Each participating family included one mother and one child—either female or male. They speculated that early exposure to more number words might predispose children to like mathematics. They reported the following: “An independent- samples t test revealed statistically significant differences in the percentages of overall numeric speech used when interacting with boys compared with girls, t(30) = 2.40, p < .05, d = .88. That is, mothers used number terms with boys an average of 9.49% of utterances (SD = 6.78%) compared with 4.64% of utterances with girls (SD = 4.43%)” (pp. 444–445).

a. Is this a between-groups or within-groups design? Explain your answer.

b. What is the independent variable? What is the dependent variable?

c. How many children were in the total sample? Explain how you determined this.

d. Is the sample likely randomly selected? Is it likely that the researchers used random assignment?

e. Were the researchers able to reject the null hypothesis? Explain.

f. What can you say about the size of the effect?

g. Describe how you could design an experiment to test whether exposure to more number words in preschool leads children to like mathematics more when they enter school.