Table 1 on page 200 of Original Source 18, “Birth weight and cognitive function in the British 1946 birth cohort: longitudinal population based study” (link available on the companion website), provides 95% confidence intervals for the difference in mean standardized cognitive scores for mid-range birthweight babies (3.01 to 3.50 kg) and babies in each of four other birthweight groups. The comparisons are made at various ages. For scores at age 8, the intervals are 20.42 to 20.11 for low weight (0 to 2.50 kg at birth); 20.16 to 10.03 for low- normal weight (2.51 to 3.00 kg at birth); 0.05 to 0.21 for high- normal weight (3.51 to 4.00 kg at birth); and 20.08 to 10.14 for very high-normal weight ( 4.01 to 5.00 kg at birth).
a. Write a sentence or two interpreting the interval for the low-weight group. Make sure your explanation applies to the correct population.
b. What difference value would indicate that the two means are equal in the population?
c. For which of the birthweight groups is it clear that there is a difference in the population mean standardized cognitive scores for that group and the midrange group? What criterion did you use to decide? In each case, explain whether the difference indicates that the mean standardized cognitive score is higher or lower for that group than for the midrange birthweight group.
d. Do the results of this study imply that low birth weight causes lower cognitive scores? Explain.