Suppose you are testing the hypotheses H0: md = 0 and Ha: d = 0 in a paired-design test and obtain a p-value of 0.02. Also suppose you computed confidence intervals for md. Based on the p-value which of the following is true?

A. Both a 95% confidence interval and a 99% confidence interval will contain 0.

B. A 95% confidence interval will contain 0, but a 99% confidence interval will not.

C. A 95% confidence interval will not contain 0, but a 99% confidence interval will.

D. Neither a 95% confidence interval nor a 99% confidence interval will contain 0.

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.

Refer to the previous exercise about the study of parents' perceptions of their children's size by researchers Kaufman et al. (Current Biology, 2013). Recall that the sample of 39 parents 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.

a. Is there evidence that youngest children's heights tend to be underestimated by their parents? 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. Interpret the p-value in the context of the study.

c. Using an appropriate applet or statistical software, find a 95% confidence interval for the difference. Interpret the confidence interval in the context of the study.

d. Summarize your findings, being sure to include a discussion of statistical significance, estimation (confidence), causation, and generalization in your answer. e. 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?