"Ugly Kids Get Less Attention from Parents," reported in the University of Alberta's online medical news site, states that a researcher "has shown that parents are more likely to give better care and pay closer attention to good-looking children compared to unattractive ones."25 A team of researchers observed over 400 2- to 5-yearold children with their parents in supermarkets, and independently graded each child on a scale of 1 to 10 on attractiveness. "Findings showed that 1.2 percent of the least attractive children were buckled in, compared with 13.3 percent of the most attractive youngsters."
a. The article does not mention how many children fall in the least and most attractive categories. Assume 1 in 100 least attractive children and 13 in 100 most attractive children were buckled in. Altogether, 14 children were buckled in, so how many would we expect to see buckled in for each group of 100 children if attractiveness was not a factor?
b. Complete tables of observed and expected counts.
c. Find the chi-square statistic for testing if the difference in proportions is significant.
d. Compare your chi-square statistic to 3.84 in order to decide if the difference is significant.
e. Before concluding that parents' attentiveness is influenced by their children's attractiveness, consider the possibility that causation occurs in the opposite direction, namely, that children's attractiveness is influenced by their parents' attentiveness. Explain how this could account for the differences observed. f. The article does not mention how attractiveness was assessed. Would you be more convinced of the claim presented in the article's title if attractiveness were evaluated on the basis of symmetry of facial features or if it were evaluated on the basis of grooming?
g. If researchers conclude that, in general, ugly children get less attention from parents, which process is the focus: data production, displaying and summarizing data, probability, or statistical inference?
h. If attractiveness made no difference, it would be very unlikely to observe only 1 in 100 least attractive children, compared to 13 in 100 most attractive children, buckled in. Which of the four processes is the focus here?
i. In a bar graph, the bar for proportion buckled in is much taller for the attractive children. Which of the four processes is the focus here?
j. Because this was an observational study, researchers must make every effort to take into account possible confounding variables when they design their study. Which of the four processes is the focus here?