Refer to the previous exercises about the study of parents’ perceptions of their children’s size. The researchers Kaufman et al. (Current Biology, 2013) also surveyed a sample of 38 parents about their eldest child’s height. The parents overestimated their eldest child’s height by 0.40 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 5.60 cm without strong skewness in the data.
a. Is there evidence that parents tend to either over- or underestimate eldest children’s heights? Carry out a theory-based test using an appropriate applet or statistical software. Find and report a p-value as well as a standardized statistic.
b. Using an appropriate applet or statistical soft ware, find a 95% confidence interval for the difference. Interpret the confidence interval in the context of the study.
c. Summarize your findings, being sure to include a discussion of statistical significance, causation, and generalization in your answer.
d. What assumption do you have to make about the data in order for the validity conditions of the appropriate theory-based test to be satisfied?

Data from previous exercise

In a study of parents’ perceptions of their children’s size, researchers Kaufman et al. (Current Biology, 2013) asked parents to estimate their youngest child’s height. The researchers hypothesized that parents tend to underestimate their youngest child’s size because the youngest child is the baby of the family and everybody else is the family appears bigger compared to the baby. The sample of 39 parents who were surveyed underestimated their youngest child’s height by 7.50 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 7.20 cm and the data are not strongly skewed.